Transmitter configured to provide a channel capacity that exceeds a saturation channel capacity

ABSTRACT

An embodiment of a transmitter includes a first number of antennas and a signal generator. The antennas are each spaced from another of the antennas by approximately a distance, and are configured to provide, at one or more wavelengths that are greater than twice the distance, a channel capacity that exceeds a saturation channel capacity. The signal generator is configured to generate a second number of signals each having a wavelength that is greater than twice the distance, the second number being related to a third number of signal pipes. And the signal generator is configured to couple each of the signals to a respective one of the antennas. Such a transmitter can be a multiple-input-multiple-output orthogonal-frequency-division-multiplexing (OFDM-MIMO) transmitter that can be configured to increase the information-carrying capacity of a channel (i.e., increase the channel capacity) above and beyond a saturation capacity of the channel.

If an Application Data Sheet (ADS) has been filed on the filing date ofthis application, it is incorporated by reference herein. Anyapplications claimed on the ADS for priority under 35 U.S.C. §§119, 120,121, or 365(c), and any and all parent, grandparent, great-grandparent,etc. applications of such applications, are also incorporated byreference, including any priority claims made in those applications andany material incorporated by reference, to the extent such subjectmatter is not inconsistent herewith.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is related to and/or claims the benefit of theearliest available effective filing date(s) from the following listedapplication(s) (the “Priority Applications”), if any, listed below(e.g., claims earliest available priority dates for other thanprovisional patent applications or claims benefits under 35 USC §119(e)for provisional patent applications, for any and all parent,grandparent, great-grandparent, etc. applications of the PriorityApplication(s)). In addition, the present application is related to the“Related Applications,” if any, listed below.

RELATED APPLICATIONS

U.S. patent application Ser. No. TBD, titled RECEIVER CONFIGURED TOPROVIDE A CHANNEL CAPACITY THAT EXCEEDS A SATURATION CHANNEL CAPACITY,naming Yaroslav Urzhumov as inventor, filed TBD with attorney docket no.575.002US02, is related to the present application.

U.S. patent application Ser. No. TBD, titled SYSTEM WITH TRANSMITTER ANDRECEIVER REMOTE FROM ONE ANOTHER AND CONFIGURED TO PROVIDE A CHANNELCAPACITY THAT EXCEEDS A SATURATION CHANNEL CAPACITY, naming YaroslavUrzhumov as inventor, filed TBD with attorney docket no. 575.002US03, isrelated to the present application.

U.S. patent application Ser. No. TBD, titled SYSTEM WITH TRANSMITTER ANDRECEIVER CONFIGURED TO PROVIDE A CHANNEL CAPACITY THAT EXCEEDS ASATURATION CHANNEL CAPACITY, naming Yaroslav Urzhumov as inventor, filedTBD with attorney docket no. 575.002US04, is related to the presentapplication.

If the listings of applications provided above are inconsistent with thelistings provided via an ADS, it is the intent of Applicant to claimpriority to each application that appears in the Priority Applicationssection of the ADS and to each application that appears in the PriorityApplications section of this application.

All subject matter of the Priority Applications and the RelatedApplications and of any and all parent, grandparent, great-grandparent,etc. applications of the Priority Applications and the RelatedApplications, including any priority claims, is incorporated herein byreference to the extent such subject matter is not inconsistentherewith.

SUMMARY

The following summary is illustrative only and is not intended to be inany way limiting. In addition to the illustrative aspects, embodiments,and features described above, further aspects, embodiments, and featureswill become apparent by reference to the drawings and the followingdetailed description.

An embodiment of a transmitter includes a first number of antennas and asignal generator. The antennas are each spaced from another of theantennas by approximately a distance, and are configured to provide, atone or more wavelengths that are greater than twice the distance, achannel capacity that exceeds a saturation channel capacity. That is,each antenna is spaced from at least one of the other antennas by adistance shorter than approximately half the operational wavelength suchthat the antennas are configured to provide, at the operationalwavelength, a channel capacity that exceeds a saturation channelcapacity at the operational wavelength. The signal generator isconfigured to generate a second number of signals each having awavelength that is greater than twice the antenna spacing, the secondnumber being related to a third number of signal pipes. And the signalgenerator is configured to couple each of the signals to a respectiveone of the antennas.

Such a transmitter can be a multiple-input-multiple-outputorthogonal-frequency-division-multiplexing (MIMO-OFDM) transmitter thatcan be configured to increase the information-carrying capacity of achannel (i.e., increase the channel capacity) above and beyond asaturation capacity of the channel, where the saturation capacity is thechannel capacity that would be provided by the transmitter if all of thetransmitter antennas were to present the same transmissioncharacteristics (e.g., gain, phase, polarization) to each of thereceiver antennas. Were all of the transmitter antennas to present thesame transmission characteristics to each of the receiver antennas,then, for the transmitter to be able to use all of the transmitterantennas for transmitting respective OFDM symbols, the minimum spacingbetween each of the transmitter antennas would be one half of the OFDMcarrier signal's free-space wavelength—this minimum, i.e., saturation,spacing can be deduced from the Nyquist sampling theorem and thediffraction theorem, which sets the maximum upper limit on thetransverse wavenumbers that can propagate from the transmit antennas tothe far fields of their apertures. This limitation, however, does notapply in the near field of the array. If the individual antennas of thetransmitter and/or receiver have a sufficiently high directivity,signals detected by different receiver antennas may have adistinguishable amplitude, phase, or polarization even though they areseparated by less than half a wavelength. Thus, configuring thetransmitter antennas such that they each present at least one differenttransmission characteristic to each receiver antenna allows thetransmitter antennas to be spaced apart by less than the Nyquist spacing(λ/2), which we refer to as the saturation spacing here. Consequently,for a given transmitter footprint, configuring the transmitter antennasin this manner allows the transmitter to increase the channel capacityabove the saturation capacity by using more transmitter antennas totransmit respective OFDM symbols.

Although the transmitter is described, for example purposes, as beingsuitable for use in a MIMO-OFDM system to transmit OFDM signals, thetransmitter is suitable for use in applications other than OFDM andMIMO-OFDM applications. For example, the transmitter may be used in anyapplication in which multiple signals are simultaneously transmitted orsimultaneously received.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a diagram of base and client single-input-single-outputorthogonal-frequency-division-multiplexing (SISO-OFDM)transmitter-receiver systems.

FIG. 2 is a plot of the frequencies of the subcarrier signals (solidlines) generated by the transmitting transmitter-receiver of FIG. 1, andof the frequency “slots” (dashed lines) that the modulated subcarriersignals can respectively occupy at the receiving transmitter-receiver ofFIG. 1.

FIG. 3 is a timing diagram of a sequence of OFDM training and datasymbols that the transmitter-receivers of FIG. 1 can transmit andreceive.

FIG. 4 is a timing diagram of another sequence of OFDM training and datasymbols that the transmitter-receivers of FIG. 1 can transmit andreceive.

FIG. 5 is a timing diagram of a sequence of OFDM combined training anddata symbols that the transmitter-receivers of FIG. 1 can transmit andreceive.

FIG. 6 is a diagram of two MIMO-OFDM transmitter-receivers and themultiple communication paths between their antennas, where the minimumspacing between the antennas of each transmitter-receiver is at leastone half the wavelength of the MIMO-OFDM carrier signal.

FIG. 7 is a diagram of two MIMO-OFDM transmitter-receivers and themultiple communication paths between their antennas, where the antennasof each transmitter-receiver are arrange in a one-dimensional array, andthe minimum spacing between the antennas of each transmitter-receiver isless than one half the wavelength of the MIMO-OFDM carrier signal,according to an embodiment.

FIG. 8 is a diagram of the transmitter circuitry of the MIMO-OFDMtransmitter-receiver of FIG. 7, according to an embodiment.

FIG. 9 is a diagram of the receiver circuitry of the MIMO-OFDMtransmitter-receiver of FIG. 7, according to an embodiment.

FIG. 10 is a diagram of the components of a subchannel between anantenna of a transmitting one of the MIMO-OFDM transmitter-receivers ofFIG. 7 and an antenna of a receiving one of the MIMO-OFDMtransmitter-receivers of FIG. 7, according to an embodiment.

FIG. 11 is a planar view of the antennas of the two MIMO-OFDMtransmitter-receivers of FIG. 6, where the antennas all have the sameradiation patterns.

FIG. 12 is a planar view of the MIMO-OFDM transmitter-receivers of FIG.7, where the antennas of one of the transmitter-receivers have radiationpatterns that differ from one another, and where the antennas of theother of the transmitter-receivers have radiation patterns that differfrom one another, according to an embodiment.

FIG. 13 is a planar view of the MIMO-OFDM transmitter-receivers of FIG.7, where the antennas of one of the transmitter-receivers have the samenon-omnidirectional radiation patterns and the same orientationsrelative to one another, and where the antennas of the other of thetransmitter-receivers have the same non-omnidirectional radiationpatterns and the same orientations relative to one another, according toan embodiment.

FIG. 14 is a planar view of the MIMO-OFDM transmitter-receivers of FIG.7, where at least one, but not all, antennas of one of thetransmitter-receivers has an omnidirectional radiation pattern at leastin a plane, and where at least one, but not all, antennas of the otherof the transmitter-receivers has an omnidirectional radiation pattern atleast in a plane, according to an embodiment.

FIG. 15 is a planar view of the MIMO-OFDM transmitter-receivers of FIG.7, where the antennas of one of the transmitter-receivers have the samenon-omnidirectional radiation patterns but different orientationsrelative to one another, and where the antennas of the other of thetransmitter-receivers have the same non-omnidirectional radiationpatterns but different orientations relative to one another, accordingto an embodiment.

FIGS. 16 and 17 are respective planar views of the MIMO-OFDMtransmitter-receivers of FIG. 7, where each of the antennas has anomnidirectional radiation pattern in the view plane of FIG. 16, andwhere each of the antennas has a non-omnidirectional radiation patternin the view plane of FIG. 17 (the view plane of FIG. 17 is differentfrom the view plane of FIG. 16), according to an embodiment.

FIG. 18 a diagram of a MIMO-OFDM transmitter-receiver having atwo-dimensional row-column antenna array that has a minimum spacingbetween antennas that is less than one half of the wavelength of aMIMO-OFDM carrier signal, according to an embodiment.

FIG. 19 a diagram of a MIMO-OFDM transmitter-receiver having atwo-dimensional circular antenna array that has a minimum spacingbetween antennas that is less than one half of the wavelength of aMIMO-OFDM carrier signal, according to an embodiment.

FIG. 20 a diagram of a MIMO-OFDM transmitter-receiver having athree-dimensional row-column-layer antenna array that has a minimumspacing between antennas that is less than one half of the wavelength ofa MIMO-OFDM carrier signal, according to an embodiment.

FIG. 21 a diagram of a MIMO-OFDM transmitter-receiver having an antennaarray formed from subarrays of antennas, a minimum spacing betweenantennas within each subarray being less than one half of the wavelengthof a MIMO-OFDM carrier signal, a minimum spacing between the subarraysbeing at least one half of the wavelength of the MIMO-OFDM carriersignal, according to an embodiment.

FIG. 22 is a diagram of a half-wavelength dipole antenna that issuitable for use as one or more of the antennas of the MIMO-OFDMtransmitter-receivers of FIGS. 7 and 12-21, according to an embodiment.

FIG. 23 is a diagram of the radiation pattern of the half-wavelengthdipole antenna of FIG. 22, according to an embodiment.

FIG. 24 is a diagram of a quarter-length dipole antenna with groundplane that are suitable for use as one or more of the antennas of theMIMO-OFDM transmitter-receivers of FIGS. 7 and 12-21, according to anembodiment.

FIG. 25 is a diagram of the radiation pattern of the quarter-lengthdipole antenna and ground plane of FIG. 24, according to an embodiment.

FIG. 26 is a diagram of a two-dimensional polarizing antenna that issuitable for use as one or more of the antennas of the MIMO-OFDMtransmitter-receivers of FIGS. 7 and 12-21, according to an embodiment.

FIG. 27 is a plan view of a patch antenna that is suitable for use asone or more of the antennas of the MIMO-OFDM transmitter-receivers ofFIGS. 7 and 12-21, according to an embodiment.

FIG. 28 is a side view of the patch antenna of FIG. 27, according to anembodiment.

FIG. 29 is a planar view of a radiation pattern of the patch antenna ofFIGS. 27 and 28 in the plane of FIG. 29, according to an embodiment.

FIG. 30 is a plan view of a multi-antenna-element antenna that issuitable for use as one or more of the antennas of the MIMO-OFDMtransmitter-receivers of FIGS. 7 and 12-21, according to an embodiment.

FIG. 31 is a plan view of a metamaterial antenna that is suitable foruse as one or more of the antennas of the MIMO-OFDMtransmitter-receivers of FIGS. 7 and 12-21, according to an embodiment.

FIG. 32 is a side view of the metamaterial antenna of FIG. 31, accordingto an embodiment.

FIG. 33 is a magnified plan view of a region of the metamaterial antennaof FIGS. 31 and 32, according to another embodiment.

FIG. 34 is a side view of a split-ring resonator that is suitable to be,or to form part of, an element of the metamaterial antenna of FIGS.31-33, according to an embodiment.

FIG. 35 is a side view of an open split-ring resonator that is suitableto be, or to form part of, an element of the metamaterial antenna ofFIGS. 31-33, according to an embodiment.

FIG. 36 is a side view of an open complementary split-ring resonatorthat is suitable to be, or to form part of, an element of themetamaterial antenna of FIGS. 31-33, according to an embodiment.

FIG. 37 is a side view of an electrical inductor-capacitor element thatis suitable to be, or to form part of, an element of the metamaterialantenna of FIGS. 31-33, according to an embodiment.

FIG. 38 is a flow diagram of a procedure that the MIMO-OFDMtransmitter-receivers of FIGS. 7 and 12-21 can implement for increasingthe channel capacity above the saturation channel capacity by increasingthe number of signal pipes in the channel, according to an embodiment.

FIG. 39 is a flow diagram of a procedure that the MIMO-OFDMtransmitter-receivers of FIGS. 7 and 12-21 can implement for increasingthe channel capacity above the saturation channel capacity by increasingthe number of signal pipes in the channel, according to an embodiment.

FIG. 40 is a diagram of two MIMO-OFDM transmitter-receivers that eachcan configure one or more characteristics its antennas so as to increasethe channel capacity above the saturation channel capacity by increasingthe number of signal pipes in the channel, according to an embodiment.

FIG. 41 is a flow diagram of a procedure that the MIMO-OFDMtransmitter-receivers of FIG. 40 can implement for increasing thechannel capacity above the saturation channel capacity by increasing thenumber of signal pipes in the channel, according to an embodiment.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof. In the drawings,similar symbols typically identify similar components, unless contextdictates otherwise. The illustrative embodiments described in thedetailed description, drawings, and claims are not meant to be limiting.Other embodiments may be utilized, and other changes may be made,without departing from the spirit or scope of the subject matterpresented here.

One or more embodiments are described with reference to the drawings,wherein like reference numerals may be used to refer to like elementsthroughout. In the following description, for purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of the one or more embodiments. It may be evident,however, that one or more embodiments may be practiced without thesespecific details. In other instances, well-known structures and devicesare shown in block-diagram form in order to facilitate describing one ormore embodiments.

Since the advent of telegraph and radio, scientists and engineers havebeen trying to discover new techniques for increasing the amount ofinformation that can be carried by an electromagnetic signal propagatingover a communication channel.

The theoretical maximum amount of information that an electromagneticsignal can carry over a given communication channel, i.e., the maximumchannel capacity, is given by the Shannon-Hartley theorem, which isrepresented by the following equation:

$\begin{matrix}{C = {B \cdot {\log_{2}\left( {1 + \frac{S}{n}} \right)}}} & (1)\end{matrix}$

where C is the channel capacity in bits/second (bits/s), B is thepassband bandwidth in Hertz (Hz) of a modulated signal, S is the averagereceived signal power in Watts (W) over the passband bandwidth, n is theaverage noise or interference in W over the passband bandwidth, and S/nis the signal-to-noise ratio (SNR) of the transmitted electromagneticcommunication signal to the Gaussian noise interference expressed as alinear power ratio.

Although an in-depth analysis and discussion of the Shannon-Hartleytheorem is omitted from this disclosure for brevity, one can see fromequation (1) that to increase the channel capacity, he/she can increasethe passband bandwidth B of the modulated signal, the signal power Pwith which the communication signal is transmitted (to increase theaverage received signal power 5), or both the passband bandwidth B andthe transmitted signal power.

One can also see from equation (1) that increasing the passbandbandwidth B provides “more bang for the buck” than increasing thereceived signal power S (by increasing the transmitted signal power P).Increasing the bandwidth B provides, at least theoretically, a linearincrease in the channel capacity C. For example, doubling the bandwidthB doubles the channel capacity C, tripling the bandwidth B triples thechannel capacity C, quadrupling the bandwidth B quadruples the channelcapacity C, and so on. But increasing the received signal power Sprovides, for signal-to-noise ratio greater than one, only a logarithmicincrease in the channel capacity C. For example, assume that S=n=1 W. Todouble the channel capacity C one would need to triple the receivedsignal power S (S=3), to triple the channel capacity C one would need toincrease the received signal power S by a factor of 7 (S=7), and toquadruple the channel capacity C, one would need to increase thereceived signal power S by a factor of 15 (S=15)!

Consequently, scientists and engineers have developed techniques tolinearly increase the channel capacity of a communication channel byeffectively increasing the passband bandwidth B of theinformation-carrying electromagnetic signal.

Referring to FIGS. 1-5, one such technique isorthogonal-frequency-division multiplexing (OFDM).

FIG. 1 is a diagram of a single-input-single-output (SISO)-OFDM basetransmitter-receiver 10 and of a SISO-OFDM client transmitter-receiver12, which communicates with the base transmitter receiver over awireless communication channel 14 via OFDM signals. For example, thebase 10 may be a wireless router in a home or office, and the client 12may be a computer, tablet, or smart phone that communicates with thebase via OFDM signals. The base 10 includes one or more antennas 16, andthe client 12 includes one or more antennas 18. SISO means that the base10 uses only one antenna 16 for signal transmission and signalreception, and that the client 12 uses only one antenna 18 for signaltransmission and signal reception. Therefore, each antenna 16 of thebase 10 may function as only a transmit antenna, as only a receiveantenna, or as a transmit-receive antenna. For example, in the formertwo cases, the base 10 includes two antennas 16, one for transmittingand one for receiving, and in the latter case, the base includes asingle antenna 16 for both transmitting and receiving. Similarly, eachantenna 18 of the client 12 may function as only a transmit antenna, asonly a receive antenna, or as a transmit-receive antenna.

FIG. 2 is a frequency plot of a portion of an OFDM signal transmittedand received by the base 10 and client 12 of FIG. 1. As described inmore detail below, an OFDM signal includes multiple subcarrier signals,and, therefore, linearly increases the channel capacity C by increasingthe passband bandwidth B, at least theoretically, up to a factor equalto the number of subcarrier signals. For example, if the OFDM signalincludes N subcarrier signals, then, at least theoretically, the OFDMsignal can increase the channel capacity by a factor of N as compared toa signal having only a single carrier signal (N=1). Or, viewed anotherway, an OFDM signal divides the channel into N subchannels each having amaximum capacity given by equation (1).

In more detail, FIG. 2 is a frequency plot of some of the N subcarriersignals (here, the subcarrier signals N−a to N−(a−8) are shown in solidline and are hereinafter called “subcarriers”) of an OFDM symbol 20,which may be transmitted by the base 10 and received by the client 12 ofFIG. 1, or vice-versa (as further described below in conjunction withFIGS. 3-5, an OFDM symbol is a time-domain portion of an OFDM signal inwhich the subcarriers are modulated with the same respective informationfor a symbol period T_(s)). Each of the subcarriers N−a to N−(a−8) has arespective frequency f_(N-a) to f_(N-(a-8)), and is orthogonal to theother subcarriers. In this context, “orthogonal” means that, in theabsence of inter-carrier interference (discussed below), noise, andother distortion, one may construct a time-domain signal from thesemodulated subcarriers (e.g., using an Inverse Fast Fourier Transform(IFFT)), and then extract these modulated subcarriers, and theinformation that they carry, from the time domain signal (e.g., using aFast Fourier Transform (FFT)) with no loss of information. Furthermore,although the base 10 is described as transmitting the OFDM signal to theclient 12 in the example below, it is understood that this example wouldbe similar if the client were transmitting the OFDM signal to the base.

Referring to FIGS. 1-2, the transmitter of the base 10 modulates each ofat least some of the N subcarriers with a respective information valuefor a time period T_(s), which is hereinafter called a symbol period—thetransmitter may not use one or more of the N subcarriers due to, forexample, excessive interference at the frequencies of these subcarriers.Examples of suitable subcarrier-modulation techniques include binaryphase-shift keying (BPSK), quadrature phase shift keying (QPSK), andquadrature amplitude modulation (QAM). In the latter two schemes, eachsubcarrier has two sinusoidal components at the subcarrier frequency, acomponent at 0° phase (e.g., cos ωt) and an orthogonal component at ±90°phase (e.g., ±sin ωt), and each component can be amplitude modulatedsuch that the subcarrier carries multiple bits of information. Forexample, using the modulation technique 256 QAM, each subcarriercomponent carries four bits of information such that each subcarriercarries eight bits of information.

Then, the transmitter of the base 10 modulates an OFDM carrier signalhaving a frequency f_(c) (and wavelength λ_(c)) with the N subcarriersto generate an OFDM signal, and transmits this OFDM signal to the client12. Modulating the OFDM carrier signal with the modulated OFDMsubcarriers effectively shifts the N subcarriers (the baseband OFDMsignal) up to f_(c). Example values for f_(c) include 2.4 GHz, 3.6 GHz,4.9 GHz, 5.0 GHz, 5.9 GHz, and 60 GHz, which are specified by the IEEE802.11 standard.

Still referring to FIGS. 1-2, the frequency spacing f_(s) betweenadjacent ones of the N subcarriers is typically constant, and isconventionally selected to minimize inter-carrier interference (ICI),which is a phenomenon that occurs if energy from one subcarrier “spillsover” to the frequency slot of another subcarrier at the receiver of theclient 12. At the transmitter of the base 10, each of the active ones ofthe N subcarriers has a frequency f_(k) (for k:0 to N−1) represented bya respective one of the solid lines (only the frequencies f_(k) fork=N−a to N−(a−8) are shown in FIG. 2), and the bandwidth associated witheach subcarrier is f_(k)±the frequency of the information signal thatmodulates the subcarrier (typically small compared to f_(k)). But at thereceiver of the client 12, the respective bandwidth associated with eachsubcarrier frequency f_(k) may be effectively shifted within arespective frequency slot 22 indicated by the dashed lines (only theslots 22 of the frequencies f_(k) for k=N−a to N−(a−8) are shown in FIG.2). For example, at the receiver of the client 12, the bandwidthassociated with the frequency f_(N-a) of the subcarrier k=N−a may beshifted to another location within the frequency slot 22 _(N-a), or maybe “spread” over multiple locations within this frequency slot. Causesfor this frequency shifting/spreading may include, for example, theexistence of multiple transmission paths within the channel and theexistence of channel conditions (e.g., humidity, temperature) that mayeffectively shift the respective phase and attenuate the respectiveamplitude of one or more of the modulated subcarrier. But as long as thebandwidth associated with one subcarrier k does not spill over into theslot 22 of another subcarrier k, or there is minimum spillage, then thereceiver of the client 12 can recover the information transmitted by thetransmitter of the base 10.

FIG. 3 is a time plot of an OFDM signal 30, which includes data symbols32 and training symbols 34 each having a duration of one symbol periodT_(s). Each data symbol 32 carries the useful information, i.e., data,to be transmitted to a receiver, and is the combination of all of thedata information (i.e., data subsymbols) that modulate the respectivesubcarriers k during a data-symbol period T_(s). Furthermore, theinformation carried by each data symbol 32 is unknown to the receiverahead of time (i.e., a priori). In contrast, each training symbol 34carriers information that is known a priori at the receiver and allowsthe receiver to determine the state of the channel, i.e., to estimatethe effects (e.g., phase shift, attenuation) that channel imparts to theOFDM signal at each of the subcarrier frequencies f_(k). Similar to adata symbol 32, each training symbol 34 is the combination of all thetraining information (i.e., training subsymbols) that modulate therespective subcarriers during a training-symbol period T_(s).

Referring to FIGS. 1-3, to allow the receiver of the client 12 torecover the transmitted data subsymbols 32 in the presence of ICI andother interference or noise, the transmitter of the base 10 transmits anOFDM training symbol 34 shortly before transmitting each OFDM datasymbol 32. That is, the transmitter of the base 10 transmits a trainingsymbol 32 during a first OFDM symbol period, and transmits a data symbol32 during a second, subsequent OFDM symbol period. Because the receiverof the client 12 “knows” the identity of the transmitted training symbol34 a priori, the receiver characterizes the channel 14 by comparing thereceived training symbol with the known transmitted training symbol 34(the received training symbol typically differs from the transmittedtraining symbol due to the phase shift, attenuation, noise, and otherdistortion introduced to the OFDM signal by the channel). For example,the receiver can characterize the channel 14 by generating an N×N matrixĤ of estimated complex frequency-domain coefficients that respectivelyrepresent the estimated frequency response (e.g., the imparted ICI,amplitude attenuation, and phase shift) of the channel at each of thesubcarrier frequencies f_(k)—the “̂” indicates that Ĥ is an estimate ofthe actual channel matrix H. The receiver of the client 12 can then usethis channel estimation matrix Ĥ to recover the transmitted data symbol32 from the respective received data symbol (the received data symboltypically differs from the transmitted data symbol due to the phaseshift, attenuation, noise, and other distortion introduced to the OFDMsignal by the channel).

FIG. 4 is a time plot of an OFDM signal 40 in which a training symbol 34is transmitted once every A data symbols 32, where A>1. Because the OFDMsignal 40 includes more data symbols 32 per training symbol 34 than doesthe OFDM signal 30 of FIG. 3, for a given signal bandwidth, signalpower, and channel conditions, the OFDM signal 40 can have a higher datathroughput than the OFDM signal 30. The OFDM signal 40 may be suitable,for example, in applications where the channel conditions are relativelystatic, i.e., change relatively slowly over time, compared to the symbolperiod T_(s).

FIG. 5 is a time plot of an OFDM signal 50 in which subcarriers carryingtraining information (hereinafter called pilot subcarriers) are combinedwith subcarriers carrying data (hereinafter called data subcarriers) toform combined symbols 52. The OFDM signal 50 may be suitable, forexample, in applications where the channel conditions are relativelydynamic, i.e., change relatively rapidly over time, compared to thesymbol period T_(s). For example, the OFDM signal 50 may be suitablewhere the base 10 and client 12 of FIG. 1 are moving relative to oneanother.

Referring to FIGS. 1-5, in addition to increasing the channel capacitylinearly as compared to a single-carrier technique, OFDM techniques canhave other benefits. Because the passband bandwidth of each subchannel(each subchannel is the respective portion of the channel 14 thatcorresponds to a respective subcarrier k) is relatively narrow, eachsubchannel can often be modeled as a flat-fading subchannel, which meansthat the subchannel can be modeled as having constant (i.e., non-timevarying) attenuation, phase shift, noise, and other distortion over thesymbol period T_(s). The ability to model each subchannel as aflat-fading subchannel can simplify the channel-estimation procedure,and can decrease the error rate inherent in the recovery of data from anOFDM data symbol. Furthermore, an OFDM signal can be more tolerant ofnarrow-band interference than a single-carrier technique. For example,if there is interference that renders one or more OFDM subcarriers kunusable to carry information, then the OFDM transmitter can stilltransmit information on the other OFDM subcarriers k.

Referring again to equation (1), one way to further increase the channelcapacity using an OFDM technique is to increase the number N ofsubcarriers k. Theoretically, as long as the transmission power of eachsubcarrier k remains the same regardless of the number N of subcarriers,the channel capacity C can increase linearly with N. That is:

$\begin{matrix}{C = {\sum\limits_{k = 0}^{k = {N - 1}}{B_{k}{\log_{2}\left( {1 + \frac{S_{k}}{n_{k}}} \right)}}}} & \left. 2 \right)\end{matrix}$

where C is the total OFDM channel capacity in bits/s), B_(k) is thepassband bandwidth in Hz of the modulated k^(th) subcarrier, S_(k) isthe average received signal power in W over the passband bandwidth forthe modulated k^(th) subcarrier, and n_(k) is the average noise orinterference in W over the passband bandwidth for the modulated k^(th)subcarrier.

Although increasing the number N of OFDM subcarriers k to increase thechannel capacity C may work in theory, in practice a transmittertypically cannot arbitrarily continue to maintain the same transmittedsignal power for each subcarrier k added to an OFDM signal. The totaltransmission power P_(total) of an OFDM transmitter is typically limitedto a maximum value P_(max) such that with the addition of eachsubcarrier k, the transmission power P_(k) per subcarrier k drops sothat the total transmission power P_(total) remains constant at P_(max).Although adding subcarriers k can still increase the channel capacity Cwhere the total transmission power is limited (this is because thechannel capacity C increases linearly with the addition of eachsubcarrier k, but decreases only logarithmically with a correspondingreduction in the per-subcarrier received power S_(k)), at some point thetransmission power P_(k) per subcarrier k will become so low that theaddition of additional subcarriers k will not increase the channelcapacity C, and may actually decrease the channel capacity because thereis too little transmission power per subcarrier.

But as described below in conjunction with FIG. 6, engineers andscientists have discovered that they can further increase the channelcapacity C by using a multiple-input-multiple-output (MIMO)-OFDMtechnique, which leverages the diversity of the communication channel toincrease the channel capacity beyond the channel capacity of an OFDMtechnique while still transmitting within the same passband B as an OFDMtechnique using a same number N of subcarriers k.

FIG. 6 is a diagram of a MIMO-OFDM system 60, which includes twoMIMO-OFDM transmitter-receivers 62 and 64, and of the portion 66 of thecommunication channel between the transmitter-receivers. Thetransmitter-receivers 62 and 64 respectively include transmit-receivecircuitry 68 and 70 and antennas 72 and 74, the channel portion 66includes subchannel portions 76 each located between a respective pairof antennas 72 and 74, and the minimum spacing between the antennas 72and the minimum spacing between the antennas 74 is at least one half thewavelength

$\left( \frac{\lambda_{c}}{2} \right)$

of the MIMO-OFDM carrier signal at frequency f_(c). The differencesbetween the subchannel portions 76 and the subchannels and the channelportion 66 and the channel, and the reason for the minimum antennaspacing of

$\frac{\lambda_{c}}{2},$

are described below. Furthermore, for example purposes, it is assumedthat the transmitter-receiver 62 is transmitting MIMO-OFDM signals withthe antennas 72, and that the transmitter-receiver 64 is receiving thetransmitted signals with the antennas 74, it being understood that thebelow description would be similar if the transmitter-receiver 64 wheretransmitting the signals and the transmitter-receiver 62 were receivingthe signals. Moreover, it is assumed that the number T of transmittingantennas 72 is equal to the number R of receiving antennas 74.

Each subchannel portion 76 includes Z>1 communication paths L, where Zis an integer with a typical range 2≦Z≦10. The paths L are typicallycaused by one or more objects (e.g., furniture, walls, people) that arelocated between, or otherwise near, the antennas 72 and the antennas 74and that scatter and redirect the MIMO-OFDM signals transmitted from theantennas 72. For example, the subchannel portion 76 _(0,0) includes Zcommunication paths L₀-L_(Z-1). That is, the MIMO-OFDM signaltransmitted from the antenna 72 ₀ traverses each path L₀-L_(Z-1) of thesubchannel portion 76 _(0,0) to arrive at the antenna 74 ₀ such that theantenna 74 ₀ receives Z versions of the signal transmitted from theantenna 72 ₀. Typically, the receiver 64 distinguishes the communicationpaths L₀ L_(Z-1) from one another by the time delay (hereinafter “pathdelay”) that each path L₀-L_(Z-1) imparts to the signal transmitted bythe antenna 72 ₀. For example, assuming that L₀ is the shortest path,the path delay that the path L₀ imparts to the signal transmitted fromthe antenna 72 ₀ is considered to be zero, and the path delays impartedto the transmitted signal by the other paths L₁-L_(Z-1) are given valuesthat indicate how much longer they are than the path delay of L₀. Forexample, L₁ may have a path delay of 0.25 microseconds (μs) because ittakes the version of the signal transmitted from the antenna 72 ₀ alongthe path L₁ an additional 0.25 μs to arrive at the antenna 74 ₀ ascompared to the time it takes the version of the signal transmittedalong the path L₀ to arrive at the antenna 74 ₀. Furthermore, ifmultiple paths L have the same delay, then the receiver 64 treats thesepaths as a single path L. Moreover, because the path-causing objects maymove over time (or the transmitter 62 and the receiver 64 may moverelative to one another over time), the receiver 64 may periodicallyrecalculate the number Z, and path delays, of the paths L in eachsubchannel portion 76. Alternatively, the receiver 64 may assume thatthe number Z, and the path delays, of the paths L are fixed; forexample, a look-up table (LUT) of the transmitter-receiver circuitry 68may store values for Z and path delays for a number of differentapplications (e.g., use as, or as part of, a stationary wireless router,and use as, or as part of, a mobile device) of the receiver 64.

Still referring to FIG. 6, a property of the described MIMO-OFDMtechnique is that each receive antenna 74 ₀-74 _(R-1) receives, overrespective subchannel portions 76, the MIMO-OFDM signals transmitted byeach of the transmit antennas 72 ₀-72 _(T-1). For example, the receiveantennas 74 ₀-74 _(R-1) receive the MIMO-OFDM signal transmitted fromthe transmit antenna 72 ₀ over the subchannel portions 76 _(0,0)-76_(0,R-1), respectively (only the subchannel portions 76 ₀ and 76_(0,R-1) are shown in FIG. 6), receive the signal transmitted from thetransmit antenna 72 ₁ (not shown in FIG. 6) over the subchannel portions76 _(1,0)-76 _(1,R-1), respectively (not shown in FIG. 6), . . . , andreceive the signal transmitted from the transmit antenna 72 _(T-1) overthe subchannel portions 76 _(T-1,0)-76 _(T-1,R-1), respectively (onlythe subchannel portions 76 _(T-1,0) and 76 _(T-1,R-1) are shown in FIG.6).

Furthermore, the collection of subchannel portions 76 over which asignal transmitted by a transmit antenna 72 propagates to the receiveantennas 74 is hereinafter referred to as a signal-pipe portion (thedifference between a signal-pipe portion and a signal pipe is describedbelow). For example, a signal-pipe portion 0 includes all of thesubchannel portions 76 between the transmit antenna 72 ₀ and each of thereceive antennas 74 ₀-74 _(R-1), a signal-pipe portion 1 includes all ofthe subchannel portions 76 between the transmit antenna 72 ₁ (not shownin FIG. 6) and each of the receive antennas 74 ₀-74 _(R-1), . . . , anda signal-pipe portion T−1 includes all of the subchannel portions 76between the transmit antenna 72 _(T-1) and each of the receive antennas74 ₀-74 _(R-1).

Therefore, the maximum number of signal-pipe portions that the channelportion 66 can support is equal to the number T of transmit antennas,and, at least in theory, a signal-pipe portion exists for a transmitantenna 72 as long as there is at least one viable subchannel portion 76between the transmit antenna and at least one of the receive antennas74.

Still referring to FIG. 6, a benefit of a MIMO-OFDM technique is thateach transmit antenna 72 can transmit a respective data symbol (e.g., adata symbol 32 of FIGS. 3-4) over the same N subcarriers k as the othertransmit antennas. That is, instead of transmitting just one data symbolover a set of N subcarriers k as in the SISO-OFDM technique describedabove in conjunction with FIGS. 1-5, a MIMO-OFDM technique allows thetransmitter-receiver 62 to transmit up to T respective data symbols overthe same set of N subcarriers k. It can be shown that under certainconditions, the Shannon-Hartley capacity formula for a MIMO-OFDM system,such as the MIMO-OFDM system 60, is given by the following equation:

C=T·B·log₂(1+ρ)  (3)

where T is the number of transmit antennas and ρ is the sum of the SNRsassociated with the individual subchannel portions 76. The conditionsunder which this equation holds true include that the number T oftransmit antennas equals the number R of receive antennas, thechannel-state information (e.g., the attenuations and phase shiftsimparted by the subchannels) is known at the receiver, the eigenvaluesof the singular value decomposition (SVD) of the channel-estimationmatrix Ĥ are equal and are such that the channel does not attenuate anyof the transmitted signals more than a threshold amount, and thechannel-estimation matrix Ĥ is effectively full rank.

So, in other words, a MIMO-OFDM technique allows a linear increase, byup to a factor of T, of the channel capacity C; that is, a MIMO-OFDMsystem can be thought of as a system including T SISO-OFDM systems.

Although a rigorous mathematical derivation and discussion of equation(3) is omitted for brevity, a more detailed derivation and discussioncan be found in Hampton, J., Introduction to MIMO Communications,Cambridge University Press 2014, which is incorporated by reference inits entirety.

Using a MIMO-OFDM technique to increase the channel capacity C by up toa factor of T as described above is often called spatial multiplexing,and the ability to spatially multiplex respective data symbols from T>1transmit antennas depends on the diversities and the gains (in thecontext of this disclosure, gain is the inverse of attenuation) of thesubchannels as described below.

The following are examples to illustrate the above points.

Still referring to FIG. 6, for example purposes, assume that theMIMO-OFDM system 60 is a 2×2 system, which means that the systemincludes T=2 two transmit antennas 72 ₀-72 ₁ (also labeled T₀ and T₁below) and R=2 two receive antennas 74 ₀-74 ₁ (also labeled R₀ and R₁below), and that the channel portion 66 between the transmit and receiveantennas imparts only a gain (no phase shift, no noise, and no otherdistortion) to the transmitted signals. Further assume that thetransmitter 62 can transmit data symbols each having one of thefollowing values: 0, 1, 2, 3, and 4.

In a first example, it is assumed that the communication channel has nodiversity, the antenna T₀ transmits a data symbol DS₀, the antenna T₁transmits a data symbol DS₁, and the combined signal power that thereceive antennas R₀ and R₁ together receive from each of the transmitantennas T₀ and T₁ is the same (this indicates that the eigen values ofthe above-mentioned singular value decomposition of the estimatedchannel matrix are equal). The estimated channel matrix Ĥ is as follows:

R₀ R₁ T₀ H_(0, 0) = 2 H_(0, 1) = 2 T₁ H_(1, 0) = 2 H_(1, 1) = 2where H_(0,0) is the normalized channel gain of the subchannel thatincludes the subchannel portion 76 ₀ between the antennas T₀ and R₀,H_(0,1) is the normalized channel gain of the subchannel that includesthe subchannel portion 76 _(0,1) between the antennas T₀ and R₁, H_(1,0)is the normalized channel gain of the subchannel that includes thesubchannel portion 76 _(1,0) (not shown in FIG. 6) between the antennasT₁ and R₀, and H_(1,1) is the normalized channel gain of the subchannelthat includes the subchannel portion 76 _(1,1) (not shown in FIG. 6)between the antennas T₁ and R₁ (although the subchannel gains in thisexample are shown being greater than one to simplify the example, inactuality the gains are typically less than one). The channel thatincludes the channel portion 66 has no diversity because the subchannelgains H_(0,0), H_(0,1), H_(1,0), and H_(1,1) are all equal to the samevalue 2.

Continuing with the example, the receiver 64 obtains the following twoequations, one from each receive antenna R₀ and R₁, where the MIMO-OFDMsignals received by the receive antennas R₀ and R₁ are labeled u₀ andu₁, respectively:

u ₀=8=DS ₀ ·H _(0,0) +DS ₁ ·H _(1,0)  4)

u ₁=8=DS ₀ ·H _(0,1) +DS ₁ ·H _(1,1)  5)

Because H_(0,0)=H_(0,1)=H_(1,0)=H_(1,1)=2, one can divide both sides ofequations (4) and (4) by 2 to obtain the following equations:

u ₀/2=4=DS ₀ +DS ₁  6)

u ₁/2=4=DS ₀ +DS ₁  7)

Although there are two equations with two unknowns, one cannot obtainunique solutions for DS₀ and DS₁ because equations (6) and (7) arelinearly dependent on one another. That is, any of the following pairsof values of DS₀ and DS₁ are solutions to equations (6) and (7): DS₀=0and DS₁=4, DS₀=1 and DS₁=3, DS₀=2 and DS₁=2, DS₀=3 and DS₁=1, and DS₀=4and DS₁=0. Because the receiver 64 only “cares” about recovering thecorrect pair of data symbols DS₀ and DS₁, the last two of thesepossibilities can be eliminated; but this still leaves the followingthree possible value pairs for DS₀ and DS₁: 0 and 4, 1 and 3, and 2 and2. Because there are multiple solutions for the values of DS₀ and DS₁,the receiver 64 cannot accurately determine the values of DS₀ and DS₁.

In a second example, all of assumptions of the first example hold exceptthat it is assumed that the communication channel has partial diversity,not zero diversity. The estimated channel matrix Ĥ is as follows:

R₀ R₁ T₀ H_(0, 0) = 2 H_(0, 1) = 6 T₁ H_(1, 0) = 1 H_(1, 1) = 3The channel has partial diversity in this example because the subchannelgains H_(0,0), H_(0,1), H_(1,0), and H_(1,1) are not equal.

In this example, the receiver 64 obtains the following two equationsfrom the receive antennas R₀ and R₁:

u ₀=8=DS ₀ ·H _(0,0) +DS ₁ ·H _(1,0)=2·DS ₀+6·DS ₁  8)

u ₁=4=DS ₀ ·H _(0,1) +DS ₁ ·H _(1,1)=1·DS ₀+3·DS ₁  9)

Dividing equations (8) and (9) by 2 yields the following equations:

u ₀=4=DS ₀+3·DS ₁  10)

u ₁=4=DS ₀+3·DS ₁  11)

Although there are two equations with two unknowns, unique solutions forDS₀ and DS₁ cannot be obtained because equations (10) and (11) arelinearly dependent on one another. That is, any of the following pairsof values of DS₀ and DS₁ are solutions to equations (10) and (11): DS₀=1and DS₁=1, and DS₀=4 and DS₁=0. Again, because there are multiplesolutions to equations (10) and (11), the receiver 64 cannot accuratelydetermine the values of DS₀ and DS₁.

In the above two examples, because the equations yielded by theestimated channel matrix Ĥ are linearly dependent on one another, and,therefore, cannot provide a unique solution for DS₀ and DS₁, the rowsand columns of Ĥ are said to be linearly dependent on one another.

Consequently, the estimated channel matrices Ĥ in the above examples aresaid to have a rank r that is less than full rank, because full rankwould be r=2, but the actual rank r=1.

It can be shown that the rank r of an estimated channel matrix Ĥdictates how many respective data symbols DS a MIMO-OFDM system cantransmit and receive. Per above, the maximum number of respective datasymbols that a MIMO-OFDM system can transmit and receive during a samesymbol period is equal to the number T of transmit antennas. Therefore,when the estimated channel matrix Ĥ is full rank, it has a rank r=T. Butif the estimated channel matrix Ĥ has a rank r that is less than fullrank, then the MIMO-OFDM system can transmit simultaneously only rrespective data symbols even if T>r. That is, in effect, when theestimated channel matrix Ĥ is less than full rank, at least one of thetransmit antennas is “wasted” in the sense that it cannot be used tosend a respective data symbol—the “wasted” transmit antenna can be usedto transmit a same data symbol as another transmit antenna, but thistechnique, called spatial diversity, is not discussed herein, although adescription of this technique is described in Hampton, J., Introductionto MIMO Communications, Cambridge University Press 2014, which isincorporated by reference in its entirety.

Still referring to FIG. 6, In a third example, all of assumptions of thefirst and second examples hold except that it is assumed that thecommunication channel has full diversity, and, therefore, is of fullrank r=2. The estimated channel matrix Ĥ is as follows:

R₀ R₁ T₀ H_(0, 0) = 2.25 H_(0, 1) = 3.87 T₁ H_(1, 0) = 1.62 H_(1, 1) =2.43It can be shown that the above estimated channel matrix Ĥ yields twoequations that can be solved to yield unique solutions for the datasymbols DS₀ and DS₁ at the receiver. Therefore, unlike in the previoustwo examples, the channel matrix of this third example would allow aMIMO-OFDM system to transmit T=2 respective data symbols DS₀ and DS₁simultaneously from two transmit antennas 72 ₀ and 72 ₁.

But even if the effective channel matrix Ĥ is full rank, it still maynot allow a MIMO-OFDM system to transmit a number of respective datasymbols equal to the number T of transmit antennas.

Consider the following example estimated channel matrix Ĥ:

R₀ R₁ T₀ H_(0, 0) = 2.01 H_(0, 1) = 6.04 T₁ H_(1, 0) = 1.10 H_(1, 1) =3.07

Although from a precise mathematical standpoint the rows and columns ofthis matrix are not linearly dependent one on another, they are so closeto being linearly dependent that in an actual MIMO-OFDM system, withnoise, distortion, etc., the estimated channel matrix Ĥ is “too close”to having a rank of only r=1 one that the receiver 64 would be unable toyield two equations from which the receiver could obtain uniquesolutions for DS₀ and DS₁.

This result gives rise to the concept of an estimated channel matrix Ĥthat is effectively full rank, or has an effective full rank, whichmeans that the rows and columns are linearly independent from oneanother by a sufficient margin to allow the receiver 64 to obtain uniquesolutions for DS₀ and DS₁. Using the third example above, this margin,m, may be determined according to the following equation:

m=√{square root over ((0.01−0.10)²+(0.04−0.07)²)}  12)

which effectively quantizes the difference between the rows of theestimated channel matrix Ĥ being linearly independent and being linearlydependent.

If m is greater than a threshold Threshold_(margin), then the estimatedchannel matrix Ĥ has an effective full rank. The thresholdThreshold_(margin) can be determined according to the particularapplication, and according to other parameters such as the minimum SNRspecified by the receiver 64.

But even if the estimated channel matrix Ĥ is effectively full rank, itstill may not allow a MIMO-OFDM system to transmit simultaneously anumber of data symbols equal to the number T of transmit antennas.

Consider the following example estimated channel matrix Ĥ, which iseffectively full rank:

R₀ R₁ T₀ H_(0, 0) = .01 H_(0, 1) = .04 T₁ H_(1, 0) = .20 H_(1, 1) = .07

Even though the estimated channel matrix Ĥ is effectively full rank, thegains of the subchannels between the transmitter and receiver are so lowthat by the time the transmitted signals arrive at the receive antennas,the respective powers of the transmitted signals are so low that they donot meet the minimum SNR threshold that the receiver needs to recoverthe transmitted data symbols DS₀ and DS₁ from the received signals.

This result gives rise to the concept of an estimated channel matrix Ĥthat has large enough gain (or, conversely, small enough attenuation) toallow transmitted signals to reach the receiver with sufficient receivedsignal power. Using the above example estimated channel matrix Ĥ, onecan determine the power gains corresponding to each of the transmitantennas according to the following equations:

Power gain corresponding to T ₀=/√{square root over((0.01)²+(0.04)²)}  13)

Power gain corresponding to T ₁=√{square root over((0.20)²+(0.07)²)}  14)

If the power gains corresponding to T₀ and T₁ are both greater than orequal to a power-gain threshold P_(gain), then the estimated channelmatrix Ĥ has an effective full rank. If only one of the power gainscorresponding to the transmit antennas T₀ and T₁ is greater than orequal to P_(gain), then effective rank of the estimated channel matrix Ĥis less than full rank (effective rank r=1 in this example) and thetransmitter 62 can transmit only one data symbol DS at a time. And ofcourse if neither of the power gains associated with T₀ and T₁ isgreater than P_(gain), then the transmitter 62 may be unable to send anydata symbols DS to the receiver 64.

In summary, for the transmitter 62 to be able to send a respective datasymbol DS from each of its T transmit antennas 72, the estimated channelmatrix Ĥ for the communication channel including the channel portion 66must have effective full rank and have a sufficient gain for eachtransmit antenna.

Still referring to FIG. 6, it may seem that based on the abovedescription, as long as the estimated channel matrix Ĥ has effectivefull rank and sufficient gain, a designer can linearly increase theMIMO-OFDM channel capacity C by adding as many transmit and receiveantennas 72 and 74 as one can “cram” onto the transmitter 62 and thereceiver 64.

But there is a limitation to the number of antennas 72 and 74 that theMIMO-OFDM transmitter-receivers 62 and 64 can include for a giventransmitter-receiver size.

When the MIMO-OFDM receiver 64 is in the radiative far field of theMIMO-OFDM transmitter 62, it can be shown, by application of theDiffraction Theorem and the Nyquist Sampling Theorem, that the minimumspacing between the transmit antennas 72, and the minimum spacingbetween the receive antennas 74, is

$\frac{\lambda_{c}}{2},$

where, as discussed above, λ_(c) is the wavelength of the MIMO-OFDMcarrier signal at carrier frequency f_(c). That is, if, for example, twotransmit antennas 72 are spaced apart by less than

$\frac{\lambda_{c}}{2},$

then these two transmit antennas are indistinguishable from one anotherat the receiver 64, i.e., these two transmit antennas appear as a singletransmit antenna to the receiver. Likewise, if, for example, two receiveantennas 74 are spaced apart by less than

$\frac{\lambda_{c}}{2},$

then these two receive antennas are indistinguishable from one anotherat the transmitter 62, i.e., these two receive antennas appear as asingle receive antenna to the transmitter.

And when the MIMO-OFDM receiver 62 is in the radiative near field of theMIMO-OFDM transmitter 64, although the Diffraction Theorem and theNyquist Sampling Theorem do not dictate a minimum spacing of

$\frac{\lambda_{c}}{2}$

between the transmit antennas 72 and between the receive antennas 74, ithas been found that for a minimum spacing less than

$\frac{\lambda_{c}}{2},$

the channel lacks diversity, and therefore, is not full rank. That is,if two transmit antennas 72 are spaced apart by less than

$\frac{\lambda_{c}}{2},$

the lack of diversity in the communication channel causes one of thesetwo transmit antennas to be “wasted,” i.e., the transmitter 62 cannottransmit two respective data symbols via these two antennas, but cantransmit only one data symbol with these antennas.

Therefore, this minimum antenna spacing of

$\frac{\lambda_{c}}{2}$

can limit significantly the number of antennas 72 and 74 that theMIMO-OFDM transmitter-receivers 62 and 64 can respectively include. Asan example, the wavelength λ_(c) of a MIMO-OFDM carrier at 2.4 GHz (apopular frequency for devices, such as routers, compatible with the IEEE802.11 standard) is about 12.5 centimeters (cm), such that

${\frac{\lambda_{c}}{2} \approx {6\mspace{14mu} {cm}}} = {2.5\mspace{14mu} {{inches}.}}$

Therefore, a wireless router with a footprint of, for example, 5 inches(in)×7 in can include four antennas with a minimum spacing between pairsof antennas of 2.5 in. And devices (e.g., smart phones) with smallerfootprints can support even fewer antennas. Even at higher carrierfrequencies f_(c), such as the newer 60 GHz carrier frequency for802.11, the restriction as to the number of antennas that a wirelessdevice can have is significant. Referring to FIGS. 7-10, described is anembodiment of an MIMO-OFDM transmitter-receiver that can transmit andreceive respective MIMO-OFDM symbols using antennas having a minimumantenna spacing of less than

$\frac{\lambda_{c}}{2}.$

As described below, such a MIMO-OFDM transmitter-receiver leverages thatthe channel includes portions of the transmitter and receiver, includingthe transmit and receive antennas, and uses these portions to increasethe diversity of the channel to a level that allows the estimatedchannel matrix Ĥ to have a higher effective rank r than even a full-rankestimated channel matrix for a system with a minimum antenna spacingthat is greater than or equal to

$\frac{\lambda_{c}}{2}.$

FIG. 7 is a diagram of a MIMO-OFDM system 80, which includes twoMIMO-OFDM transmitter-receivers 82 and 84, and of the portion 86 of thecommunication channel between the transmitter-receivers, according to anembodiment. The transmitter-receivers 82 and 84 respectively includetransmit-receive circuitry 88 and 90 and antennas 92 and 94, the channelportion 86 includes subchannel portions 96 each located between arespective pair of antennas 92 and 94, and the minimum spacing betweenthe antennas 92 and the minimum spacing between the antennas 94 is lessthan one half the wavelength

$\left( \frac{\lambda_{c}}{2} \right)$

of the MIMO-OFDM carrier signal at frequency f_(c). The differencesbetween the subchannel portions 96 and the subchannels and the channelportion 96 and the channel, and the reason for the minimum antennaspacing of less than

$\frac{\lambda_{c}}{2},$

are described below. Furthermore, for example purposes, it is assumedthat the transmitter-receiver 82 is transmitting MIMO-OFDM signals withthe antennas 92, and that the transmitter-receiver 84 is receiving thetransmitted signals with the antennas 94, it being understood that thebelow description would be similar if the transmitter-receiver 84 wheretransmitting the signals and the transmitter-receiver 82 were receivingthe signals. Moreover, it is assumed that the number T of transmittingantennas 92 is equal to the number R of receiving antennas 94.

FIG. 8 is a diagram of an embodiment of the MIMO-OFDMtransmitter-circuitry portion 100 of the transmitter-receiver circuitry88 and 90 of FIG. 7, according to an embodiment. The transmittercircuitry 100 includes T transmit paths 102 ₀-102 _(T-1); but forbrevity, only the path 102 ₀ is described in detail, it being understoodthat the remaining paths 102 ₁-102 _(T-1) can be similar. Furthermore,for example purposes, the transmitter circuitry 100 is described belowas being part of the transmitter-receiver circuitry 88, it beingunderstood that the description of the transmitter circuitry 100 whenpart of the transmitter-receiver circuitry 90 is similar. Moreover, thetransmitter circuitry 100 can be referred to as a signal generator.

The transmit path 102 ₀ includes a symbol (data and training) generatorcircuit 104 ₀, a symbol-subcarrier-coefficient generator circuit 106 ₀,an Inverse Fourier Transform (IFFT) circuit 108 ₀, a digital-to-analogconverter (DAC) 110 ₀, and a modulator 112 ₀, which is coupled to theantenna 92 ₀ (although the antennas in FIG. 8 may also be used asreceive antennas, they are labeled as transmit antennas because thetransmitter-receiver 82 of FIG. 7 is described herein as transmittingMIMO-OFDM signals). The symbol generator circuit 104 ₀ is configured togenerate data and training sub symbols from data information andtraining information, respectively, and thesymbol-subcarrier-coefficient generator circuit 106 ₀ is configured togenerate from each sub symbol a respective complex frequency-domaincoefficient for mapping to the respective subsymbol subcarrier. The IFFTcircuit 108 ₀ is configured to transform the subsymbol-subcarriercoefficients into a digital time-domain waveform, and the DAC 110 ₀ isconfigured to convert the digital time-domain waveform into an analogtime-domain waveform. The modulator 112 ₀ is configured to modulate acarrier signal at a carrier frequency f_(c) (e.g., 2.4 GHz, 3.6 GHz, 5GHz, or 60 GHz) with the analog time-domain waveform to generate amodulated carrier signal having a bandwidth centered around f_(c). Andthe antenna 92 ₀ is configured to transmit the modulated carrier signalfor reception by a receiver such as the receiver 84 of FIG. 7.

The transmitter circuitry 100 also includes a transmit-path-and-antennaselector circuit 114, which is configured to select the transmit paths102, and thus the antennas 92, over which the transmitter circuitry 100is to transmit respective data symbols. For example, as described belowin conjunction with FIGS. 38-39 and 41, depending on the channelcapacity, the transmitter circuitry 100 may be unable to utilize all ofthe transmit paths 102 and transmit antennas 92 for transmittingrespective data symbols. In such a situation, the selector circuit 114is configured to select which transmit paths 102 and antennas 92 are tobe utilized for sending respective data symbols, and which transmitpaths and antennas are to be deactivated or utilized to send redundantdata symbols (i.e., the same data symbol as another transmit path andantenna).

FIG. 9 is a diagram of an embodiment of the MIMO-OFDM receiver-circuitryportion 120 of the transmitter-receiver circuitry 88 and 90 of FIG. 7,according to an embodiment. The receiver circuitry 120 includes Rreceive paths 122 ₀-122 _(R-1); but for brevity, only the path 122 ₀ isdescribed in detail, it being understood that the remaining paths 122₁-122 _(R-1) can be similar. Furthermore, for example purposes, thereceiver circuitry 120 is described below as being part of thetransmitter-receiver circuitry 90, it being understood that thedescription of the receiver circuitry 120, when part of thetransmitter-receiver circuitry 88, is similar.

The receive path 122 ₀ includes a demodulator 124 ₀ coupled to theantenna 94 ₀ (although the antennas in FIG. 9 may also be used astransmit antennas, they are described as receive antennas because thetransmitter-receiver 84 of FIG. 7 is described herein as receivingMIMO-OFDM signals) for demodulating the modulated carrier signalreceived by the antenna 94 ₀, an analog-to-digital converter (ADC) 126 ₀for converting the analog demodulated signal into a digital signal, anda Fourier Transform (FFT) circuit 128 ₀ for converting the time-domaindigital signal into a frequency-domain coefficients. A channel-estimatorcircuit 130, and a data-recovery circuit 132 for recovering data fromthe data symbols (and training information from the training symbols),are common to all receive paths 122.

Referring to FIGS. 7-9, as described below, unlike conventionalMIMO-OFDM transmitter-receivers, the MIMO-OFDM transmitter-receivers 82and 84 can increase the diversity of the communication channel betweenthem such that they can include antennas with a minimum spacing lessthan

$\frac{\lambda_{c}}{2}$

to achieve a higher channel capacity C, at least in the near field, ascompared to MIMO-OFDM transmitter-receivers having antennas with aminimum spacing of at least

$\frac{\lambda_{c}}{2}.$

FIG. 10 is a diagram of portions of the transmit path 102 ₀ of FIG. 8,portions of the receiver path 122 ₀ of FIG. 9, the transmit and receiveantennas 92 ₀ and 94 ₀, and the subchannel portion 96 _(0,0) between thetransmit and receive antennas.

Referring to FIG. 10, because the channel estimator circuit 130determines, e.g., the attenuation, phase shift, noise, and otherdistortion introduced to the MIMO-OFDM signal between the output of thesymbol-subcarrier coefficient generator circuit 106 ₀ and the input ofthe channel estimator circuit, the corresponding subchannel 140 _(0,0),at least as “seen” by the channel estimator, includes not only thesubchannel portion 96 _(0,0) of the channel portion 86, which is thepropagation medium between the transmit and receive antennas, but alsoincludes the IFFT 108 ₀, DAC 110 ₀, modulator 112 ₀, antennas 92 ₀ and94 ₀, demodulator 124 ₀, ADC 126 ₀, and FFT 128 ₀.

Because the subchannel 140 _(0,0) includes portions of the transmitterand receiver paths 102 ₀ and 122 ₀ and the transmit and receive antennas92 ₀ and 94 ₀, an engineer can design one or more of these path portionsand antennas to impart increased diversity to the subchannel 140 _(0,0),as compared to the other subchannels 140, such that at least when thereceive antennas are in the near field of the transmit antennas, theincreased channel diversity is sufficient to allow the antennas toincrease the channel capacity C by having a minimum spacing that is lessthan

$\frac{\lambda_{c}}{2},$

thus allowing more antennas per a given footprint of the MIMO-OFDMtransmitter-receiver. With such a technique, the diversity of thesubchannels 140 is no longer dictated by the propagation medium(subchannel portions 96) between the transmit and receive antennas 92and 94. For example, in embodiments described below, the transmit andreceive antennas 92 and 94 are configured to provide this increasedchannel diversity and channel capacity in a MIMO-OFDM system. But it iscontemplated that embodiments of the below-described techniques forincreasing channel diversity and channel capacity in a MIMO-OFDM systemcan also be used in applications other than OFDM and MIMO-OFDM. Forexample, such embodiments may be used in any application in whichmultiple signals are simultaneously transmitted or simultaneouslyreceived.

FIG. 11 is a diagram of a conventional MIMO-OFDM system 150 having twotransmit antennas 152 ₀ and 152 ₁ and two receive antennas 154 ₀ and 154₁. In this example, all of the antennas 152 and 154 have substantiallyuniform omnidirectional beam, i.e., radiation, patterns, which meansthat they have the same power gain, phase, and polarization in all, oralmost all, directions (for example, a half-wavelength dipole is anantenna that has an omnidirectional radiation pattern in all directionswithin the same plane). Such omnidirectional antennas are oftenpreferred in a conventional MIMO-OFDM transmitter-receiver because theycan radiate signal energy to, and receive signal energy from, otherMIMO-OFDM transmitter-receivers regardless of the positions of thelatter.

But it has been found that when the transmit antennas 152 ₀ and 152 ₁are spaced less than

$\frac{\lambda_{c}}{2}$

apart, the subchannel portions 156 between each transmit antenna and areceive antenna 154 have similar, or the same, state, even in the nearfield and in a rich multipath environment where the subchannel portionsinclude a relatively large number Z of paths L (see FIG. 6). That is,the gain, phase, noise, and other distortion introduced by thesubchannel portion 156 _(0,0) is similar to, or the same as, the gain,phase, noise, and other distortion introduced by the subchannel portion156 _(1,0). Similarly, the gain, phase, noise, and other distortionintroduced by the subchannel portion 156 _(0,1) is similar to, or thesame as, the gain, phase, noise, and other distortion introduced by thesubchannel portion 156 _(1,1).

Because in the above-described scenario the channel diversity isinsufficient for the estimated channel matrix Ĥ to have an effectivefull rank r=2, the estimated channel matrix has only an effective rankr=1 such that only one data symbol can be transmitted at a time fromeither or both of the transmit antennas 152 ₀ and 152 ₁.

A similar analysis applies, and yields the same result, if the receiveantennas 154 ₀ and 154 ₁ are spaced apart by less than

$\frac{\lambda_{c}}{2},$

or if both the transmitter antennas 152 ₀ and 152 ₁ and the receiveantennas 154 ₀ and 154 ₁ are spaced apart by less than

$\frac{\lambda_{c}}{2}.$

Consequently, when two or more transmit antennas each present same orsimilar transmit characteristics, i.e., transmission profiles, to eachreceive antenna, the two or more transmit antennas can only transmit asingle data symbol at a time unless the diversity of the channel issufficient to make the make the transmit antennas appear to havedifferent transmission profiles at each of the receive antennas.Although this is true regardless of the minimum spacing between theantennas and of whether the receiver is in the near field or in the farfield of the transmitter, the diversity of the channel is more likely tobe insufficient to make the transmit antennas appear to have differenttransmission profiles at each of the receive antennas when the transmitantennas and the receive antennas are spaced apart by less than

$\frac{\lambda_{c}}{2}.$

It follows, therefore, that one can define a saturation channel capacityC_(saturation) as the channel capacity provided by a MIMO-OFDMtransmitter-receiver having antennas that each present the sametransmission profile to each receive antenna during signal transmission,and that each present the same reception profile to each transmitantenna during signal reception. For example, suppose a transmitter hastwo transmit antennas with the same transmission profiles spaced atleast

$\frac{\lambda_{c}}{2}$

apart, and the channel is diverse enough to make the antennas appear tohave different transmission profiles at each of the receive antennas. Inthis example, the saturation channel capacity C_(saturation) would bethe combined capacity provided by the two transmit antennas. But if athird transmit antenna is added, and the channel is diverse enough tomake only two of the three antennas appear to have differenttransmission profiles at each of the receive antennas, thenC_(saturation) would still be the combined capacity of two transmitantennas.

Alternatively, one can define a saturation channel capacityC_(saturation) as the number of signal pipes provided by a MIMO-OFDMtransmitter-receiver having antennas that each present the sametransmission profile to each receive antenna during signal transmission,and that each present the same reception profile to each transmitantenna during signal reception.

Or, one can define a saturation channel capacity C_(saturation) as thenumber of signal pipes that equals the effective rank of an estimatedchannel matrix that represents the communication channel provided by aMIMO-OFDM transmitter-receiver having antennas that each present thesame transmission profile to each receive antenna during signaltransmission, and that each present the same reception profile to eachtransmit antenna during signal reception.

But as discussed below, by appropriately spacing and configuring thecharacteristics, and thus the profiles, of the transmit antennas 92 andthe receive antennas 94, the MIMO-OFDM transmitter-receivers 82 and 84of FIG. 7 can provide, to the communication channel between them, achannel capacity C that exceeds the saturation channel capacityC_(saturation). That is, such appropriate spacing and configuring of theantenna characteristics can actually increase the capacity C of achannel.

FIG. 12 is a diagram of the MIMO-OFDM system 80 of FIG. 7 according toan embodiment where the antennas 92 and 94 of the transmitter 82 andreceiver 84, respectively, are configured to provide a channel capacityC that exceeds the saturation channel capacity C_(saturation), and wherelike numbers reference like items relative to FIG. 7. In thisembodiment, the transmitter-receiver 82 has two antennas 92 ₀ and 92 ₁,which are spaced apart by a distance d₁ that is less than

$\frac{\lambda_{c}}{2},$

and which are configured to transmit respective MIMO-OFDM data symbolsDS₀ and DS₁. Similarly, in this embodiment, the transmitter-receiver 84has two antennas 94 ₁ and 94 ₂, which are spaced apart by a distance d₂that is less than

$\frac{\lambda_{c}}{2},$

and which are configured to receive the respective MIMO-OFDM symbols DS₀and DS₁ transmitted from the antennas 92 ₀ and 92 ₁. The distance d₁ maybe measured from an edge of the antenna 92 ₀ to an edge of the antenna92 ₁, or, may be measured between the geometrical centers, the centersof mass, the center axes, or other suitable points of the antennas 92 ₀and 92 ₁; and the distance d₂ between the antennas 94 ₀ and 94 ₁ may bemeasured similarly. Furthermore, the view of FIG. 12 is in an azimuthplane that all of the antennas 92 and 94 intersect.

The antennas 92 ₀, 92 ₁, 94 ₀, and 94 ₁ each have different respectivebeam, i.e., radiation patterns and peak directivities D

$\left( {D = \frac{1}{\left. {\frac{1}{4\pi}{\int_{0}^{2\pi}\int_{0}^{\pi}}} \middle| {F\left( {\theta,\phi} \right)} \middle| {}_{2}{\sin \ \theta \; d\; \theta \; d\; \phi} \right.}} \right.$

is along the main lobes of the radiation patterns in FIG. 12), whichcause the antennas 92 ₀ and 92 ₁ to each present a differenttransmission profile to the receive antenna 94 ₀, and to each present adifferent transmission profile to the receive antenna 94 ₁, regardlessof the diversity of the subchannel portions 96 and even though theantennas 92 ₀ and 92 ₁ are spaced apart by less than

$\frac{\lambda_{c}}{2}.$

And these different transmission profiles not only sufficientlydiversify the subchannels 140 so that the estimated channel matrix isfull rank, but also provide each subchannel 140 with sufficient gain sothat the estimated channel matrix is effective full rank. An alternativeway to view this configuration is that the different respectiveradiation patterns and peak directivities D of the antennas 92 ₀, 92 ₁,94 ₀, and 94 ₁ cause the antennas 94 ₀ and 94 ₁ to each present adifferent reception profile to the transmit antenna 92 ₀, and to eachpresent a different reception profile to the transmit antenna 94 ₁, eventhough the antennas 94 ₀ and 94 ₁ are spaced apart by less than

$\frac{\lambda_{c}}{2}.$

The straight-line path L of the subchannel portion 96 _(0,0) is along aside of a main lobe of the antenna 92 ₀ and through a main lobe of theantenna 94 ₀, where the lobes represent antenna power gain along thedirection of the lobe.

In contrast, the straight-line path L of the subchannel portion 96_(1,0) is along the edge of a minor lobe of the antenna 92 ₁ and througha minor lobe of the antenna 94 ₀.

Therefore, the gain that the antennas 92 ₀ and 94 ₀ impart to thesubchannel 140 _(0,0), which, per FIG. 10, includes these antennas andthe subchannel portion 96 _(0,0), is significantly different from thegain that the antennas 92 ₁ and 94 ₀ impart to a subchannel 140 _(1,0),which includes these antennas and the subchannel portion 96 _(1,0). Andbecause an antenna's radiation pattern typically undergoes a phase shiftof about 180° between lobe nulls (the locations between lobes where thegain is, or is approximately, zero), the phase that the antennas 92 ₀and 94 ₀ impart to the subchannel 140 _(0,0) is significantly differentfrom the phase that the antennas 92 ₁ and 94 ₀ impart to the subchannel140 _(1,0).

Similarly, the straight-line path L of the subchannel portion 96 _(0,1)is along the edge of a minor lobe of the antenna 90 ₀ and bisects a mainlobe of the antenna 92 ₁.

In contrast, the straight-line path L of the subchannel portion 96_(1,1) bisects a major lobe of the antenna 92 ₁ and is along an edge ofa minor lobe of the antenna 94 ₁.

Therefore, the gain and phase that the antennas 94 ₀ and 94 ₁ impart toa subchannel 140 _(0,1), which includes these antennas and thesubchannel portion 96 _(0,1), is significantly different from the gainand phase that the antennas 92 ₁ and 94 ₁ impart to a subchannel 140_(1,1), which includes these antennas and the subchannel portion 96_(1,1).

Consequently, the transmission profiles of the antennas 92 ₀ and 92 ₁,and the reception profiles of the antennas 94 ₀ and 94 ₁, sufficientlydiversify the subchannels 140 _(0,0), 140 _(0,1), 140 _(1,0), and 140_(1,1) such that the estimated channel matrix Ĥ has an effective fullrank r=2. This is true even though the antenna spacings

${d_{1} < {\frac{\lambda_{c}}{2}\mspace{14mu} {and}\mspace{14mu} d_{2}} < \frac{\lambda_{c}}{2}},$

and the subchannel portions 96 may be insufficiently diverse to providean estimated channel matrix of effective full rank without theadditional diversity provided by the antennas 92 and 94.

Therefore, as long as the gains of the subchannels 140 _(0,0) 140_(0,1), 140 _(1,0), and 140 _(1,1) are greater than or equal to aminimum-gain threshold Th_(gain) that allows the transmitted MIMO-OFDMsignals to have a sufficient SNR at the receive antennas 94 ₀ and 94 ₁,the transmitter 82 can transmit respective data symbols DS₀ and DS₁simultaneously via the transmit antennas 92 ₀ and 92 ₁, respectively.

Furthermore, because

${d_{1} < {\frac{\lambda_{c}}{2}\mspace{14mu} {and}\mspace{14mu} d_{2}} < \frac{\lambda_{c}}{2}},$

the channel capacity C that the transmitter 82 and receiver 84 provideto the communication channel between them is greater than the saturationchannel capacity C_(saturation), which is the capacity (e.g., the numberof signal pipes) that the transmitter and receiver would provide if theantennas 92 ₀ and 92 ₁ each presented a same transmission profile to theantennas 94 ₀ and 94 ₁, or the antennas 94 ₀ and 94 ₁ each presented asame reception profile to the antennas 92 ₀ and 92 ₁.

Still referring to FIG. 12, alternate embodiments of the MIMO-OFDMsystem 80 are contemplated. For example, d₁ may equal, or be unequal to,d₂. Furthermore, although the antennas 92 ₀ and 92 ₁ lie along a line162 that is parallel to a line 164 along which lie the antennas 94 ₀ and94 ₁, the lines 162 and 164 need not be parallel. Moreover, althoughdescribed as including two antennas 92 ₀ and 92 ₁, thetransmitter-receiver 82 may include more than two antennas 92;similarly, although described as including two antennas 94 ₀ and 94 ₁,the transmitter-receiver 84 may include more than two antennas 94. Inaddition, although the number of transmit antennas 92 is described asbeing equal to the number of receive antennas 94, the number of transmitantennas may be greater than or less than the number of receiveantennas. Furthermore, although all the antennas 92 and 94 are describedas intersecting a same plane, not all of the antennas may intersect thesame plane. Moreover, although described as diversifying the channel bydiversifying the gains and phases of the subchannels 140, the antennas92 and 94 may diversify the channel by altering other characteristics ofthe subchannels, such as the antenna polarizations. In addition,although described as each having different radiation patterns anddirectivities, some or all of the antennas 92 and 94 may have the sameradiation patterns, the same directivities, or both the same radiationpatterns and directivities as long as the antennas are oriented, orotherwise configured, such that the transmit antennas each presentdifferent transmission profiles to each of the receive antennas, andsuch that the receive antennas each present different receptioncharacteristics to each of the transmit antennas. For example, some orall of the antennas may present the same transmission/reception profilesin one or more planes, but present different transmission/receptionprofiles in one or more other planes. Furthermore, the antennas 92 and94 may have randomly determined radiation patterns, directivities, ororientations. Moreover, to provide a uniform total gain in multiple orall directions, the antennas 92 may have their major lobes oriented indifferent directions, and the antennas 94 may have their major lobesoriented in different directions. In addition, d₁ and d₂ can have anysuitable values, such as in the range of

${0.10 \cdot \frac{\lambda_{c}}{2}}\mspace{14mu} {to}\mspace{14mu} {0.90 \cdot {\frac{\lambda_{c}}{2}.}}$

Furthermore, the radiation patterns and other characteristics (e.g.,polarization) of the antennas 92 and 94 can be fixed or configurable.

FIG. 13 is a diagram of the MIMO-OFDM system 80 of FIG. 7, according toanother embodiment where the antennas 92 and 94 of the transmitter 82and receiver 84, respectively, are configured so as to provide a channelcapacity C that exceeds the saturation channel capacity C_(saturation),where like numbers reference like items relative to FIGS. 7 and 12. Thisembodiment is similar to the embodiment of FIG. 12, except that, atleast in the plane of FIG. 13, all of the antennas 92 and 94 have thesame radiation pattern, and, therefore, have the same directivity D, theantennas 92 each have the same orientation relative to the line 162, andthe antennas 94 each have the same orientation relative to the line 164.Although the antenna 92 ₀ presents to the antenna 94 ₀ the sametransmission profile that the antenna 92 ₁ presents to the antenna 94 ₁,the subchannels 96 are still sufficiently diverse from one anotherbecause the antennas 92 ₀ and 92 ₁ each present different transmissionprofiles to the antenna 94 ₀ and to the antenna 94 ₁ according to ananalysis that is similar to the analysis applied above in conjunctionwith FIG. 12.

Still referring to FIG. 13, alternate embodiments are contemplated. Forexample, the alternate embodiments of the MIMO-OFDM system 80 describedabove in conjunction with FIG. 12 can be applicable to the embodimentsof the MIMO-OFDM system 80 described in conjunction with FIG. 13.

FIG. 14 is a diagram of the MIMO-OFDM system 80 of FIG. 7 according toanother embodiment where the antennas 92 and 94 of the transmitter 82and receiver 84, respectively, are configured to provide a channelcapacity C that exceeds the saturation channel capacity C_(saturation),and where like numbers reference like items relative to FIGS. 7 and12-13. This embodiment is similar to the embodiment of FIG. 12, exceptthat, at least in the plane of FIG. 14, the antennas 92 ₀ and 94 ₁ haveomni-directional radiation patterns with directivities D=1 (D=0 dBi),and the antennas 92 ₁ and 94 ₀ have different, non-omnidirectionalradiation patterns and different directivities D from each other andfrom the antennas 92 ₀ and 94 ₁.

Still referring to FIG. 14, alternate embodiments of the MIMO-OFDMsystem 80 are contemplated. For example, the alternate embodiments ofthe MIMO-OFDM system 80 described above in conjunction with FIG. 12 canbe applicable to the embodiment of the MIMO-OFDM system described inconjunction with FIG. 14. Furthermore, the positions of the antennas 92₀ and 92 ₁ may be swapped, the positions of the antennas 94 ₀ and 94 ₁may be swapped, or the positions of the antennas 92 ₀ and 92 ₁ may beswapped and the positions of the antennas 94 ₀ and 94 ₁ may be swapped.In addition, the antennas 90 ₁ and 92 ₀ may have the samenon-omnidirectional radiation patterns and directivities as one another,at least in the plane of FIG. 14.

FIG. 15 is a diagram of the MIMO-OFDM system 80 of FIG. 7 according toanother embodiment where the antennas 92 and 94 of the transmitter 82and receiver 84, respectively, are configured to provide a channelcapacity C that exceeds the saturation channel capacity C_(saturation),and where like numbers reference like items relative to FIGS. 7 and12-14. This embodiment is similar to the embodiment of FIG. 12, exceptthat, at least in the plane of FIG. 15, all of the antennas 92 and 94have the same radiation pattern, and, therefore, have the samedirectivity D, the antennas 92 each have different orientations relativeto the line 162, and the antennas 94 each have different orientationsrelative to the line 164.

Still referring to FIG. 15, alternate embodiments of the MIMO-OFDMsystem 80 are contemplated. For example, the alternate embodiments ofthe MIMO-OFDM system 80 described above in conjunction with FIGS. 12 and14 can be applicable to the embodiments of the MIMO-OFDM system 80described in conjunction with FIG. 15. Furthermore, two or more of theantennas 92 ₀, 92 ₁, 94 ₀, and 94 ₁ can have different radiationpatterns with the same or different directivities D, at least in theplane of FIG. 15.

FIGS. 16-17 are diagrams of the MIMO-OFDM system 80 of FIG. 7 accordingto another embodiment where the antennas 92 and 94 of the transmitter 82and receiver 84, respectively, are configured to provide a channelcapacity C that exceeds the saturation channel capacity C_(saturation),and where like numbers reference like items relative to FIGS. 7 and12-15. This embodiment is similar to the embodiment of FIG. 12, exceptthat, at least in the plane of FIG. 16, all of the antennas 92 and 94have the same omnidirectional radiation pattern, and that, at least inthe plane of FIG. 17, which plane is different from the plane of FIG.16, all of the antennas 92 and 94 have different radiation patterns (theantennas 92 and 94 also have different directivities D). For example,the plane of FIG. 17 can be parallel to or perpendicular to the plane ofFIG. 16, or may intersect the plane of FIG. 16 at an angle other than90°.

Still referring to FIGS. 16 and 17, alternate embodiments of theMIMO-OFDM system 80 are contemplated. For example, the alternateembodiments of the MIMO-OFDM system 80 described above in conjunctionwith FIGS. 12 and 14-15 can be applicable to the embodiments of theMIMO-OFDM system 80 described in conjunction with FIGS. 16 and 17.Furthermore, two or more of the antennas 92 ₀, 92 ₁, 94 ₀, and 94 ₁ canhave the same non-omnidirectional radiation patterns with the same ordifferent directivities D at least in the plane of FIG. 17. Moreover,although shown having the same gains in the plane of FIG. 16, one ormore of the antennas 90 ₀, 90 ₁, 92 ₀, and 92 ₁ can have different gainsthan the other antennas.

Referring to FIGS. 12-17, the antennas 92 of the transmitter-receiver 82are described as being arranged, i.e., as forming, a one-dimensionalantenna array along a line 162; similarly, the antennas 94 of thetransmitter-receiver 84 are described as forming a one-dimensionalantenna array along a line 164.

But as described below in conjunction with FIGS. 18-21, it iscontemplated that the antennas 92 and 94 can form multi-dimensionalarrays.

FIG. 18 is a diagram of the MIMO-OFDM transmitter-receiver 82 of FIG. 7according to an embodiment where the antennas 92 are configured toprovide a channel capacity C that exceeds the saturation channelcapacity C_(saturation), and where like numbers refer to like itemsrelative to FIG. 12, it being understood that the antennas 94 of theMIMO-OFDM transmitter-receiver 84 of FIG. 7 can be configured similarly.

The transmitter-receiver 82 includes 2T antennas 92 ₀-92 _(2T-1), whichare configured in a two-dimensional array 170. The antennas 92 arearranged in two rows 172 and 174 of equal length, each row including Tof the antennas 92. Adjacent ones of the antennas 92 in each row areseparated by a uniform minimum spacing d₃, and adjacent ones of theantennas 92 in different rows are separated by a uniform minimum spacingd₄, where

$d_{3} < {\frac{\lambda_{c}}{2}\mspace{14mu} {and}\mspace{14mu} d_{4}} < {\frac{\lambda_{c}}{2}.}$

Each of the distances d₃ and d₄ can be measured from an edge of anantenna 92 to an edge an adjacent antenna 92, or, may be measuredbetween the geometrical centers, the centers of mass, the center axes,or other suitable points of adjacent antennas 92.

The antennas 92 may have radiation patterns, directivities,orientations, and other antenna characteristics according to any of theembodiments described above in conjunction with FIGS. 12-17, or may haveother radiation patterns, directivities, orientations, and antennacharacteristics as long as the antennas 92 present to other MIMO-OFDMtransmitter-receivers antenna profiles that sufficiently diversify thechannel so that the channel capacity C is greater a saturation capacityC_(saturation) of the channel.

Still referring to FIG. 18, alternate embodiments of thetransmitter-receiver 82 are contemplated. For example, although theantenna array 170 is described as having two rows 172 and 174 of Tantennas 92, it may have more than two rows with more or fewer that 2Ttotal antennas, and these rows may be arranged to form anytwo-dimensional shape such as a square, rectangle, or a triangle.Furthermore, although the antennas 92 in reach row 172 and 174 aredescribed as having a uniform minimum spacing d₃, the spacing betweenthe antennas in each row may be non-uniform, and some of the spacingsmay be greater than

$\frac{\lambda_{c}}{2}.$

Similarly, although the antennas 92 in the row 172 are aligned with theantennas in the row 174, some or all of the antennas in the row 172 maybe misaligned with the antennas in the row 174. Moreover, although theminimum spacing d₄ between antennas 92 in one row and antennas in theother row are described as being uniform and less than

$\frac{\lambda_{c}}{2},$

the minimum spacing may be greater than

$\frac{\lambda_{c}}{2}$

as long as at least some antennas in the array are spaced apart by lessthan

$\frac{\lambda_{c}}{2}.$

In addition, although the rows 172 and 174 of antennas 92 are describedas being along respective straight lines that are parallel to oneanother, the rows may not be parallel to one another, and the antennasmay be arranged in other than straight lines.

FIG. 19 is a diagram of the MIMO-OFDM transmitter-receiver 82 of FIG. 7,according to another embodiment where the antennas 92 are configured soas to provide a channel capacity C that exceeds the saturation channelcapacity C_(saturation), and where like numbers refer to like itemsrelative to FIG. 12, it being understood that the antennas 94 of theMIMO-OFDM transmitter-receiver 84 of FIG. 7 can be arranged similarly.

The transmitter-receiver 82 includes T antennas 92 ₀-92 _(T-1), whichare configured in a two-dimensional circular array 180. Adjacent ones ofthe antennas 92 are each separated by a uniform minimum circumferentialspacing

${d_{5} < {\frac{\lambda_{c}}{2}\mspace{14mu} \left( {{along}\mspace{14mu} a\mspace{14mu} {straight}\mspace{14mu} {line}} \right)}},$

and the array 180 has a diameter da₁, which may be greater than, lessthan, or equal to

$\frac{\lambda_{c}}{2}.$

Each of the distance d₅ and the diameter da₁ can be measured along astraight line from an edge of an antenna 92 to an edge of acircumferentially or diametrically adjacent other antenna 92, or, may bemeasured between the geometrical centers, the centers of mass, thecenter axes, or other suitable points of the adjacent antennas 92.

The antennas 92 can have radiation patterns, directivities,orientations, and other characteristics according to any of theembodiments described above in conjunction with FIGS. 12-17, or can haveother radiation patterns, directivities, orientations, andcharacteristics as long as the antennas 92 present to other MIMO-OFDMtransmitter-receivers antenna profiles that sufficiently diversify thechannel so that the channel capacity C is greater a saturation capacityC_(saturation) of the channel. For example, the antennas 92 can eachhave a same radiation pattern, same directivity, a same orientation, orsame other characteristics relative to a radius 182 along which theantenna lies. Or one or more of the antennas 92 can each have adifferent (e.g., randomly generated) radiation pattern, differentdirectivity, different orientations, or different other characteristicsrelative to the radius 182 along which the antenna lies.

Still referring to FIG. 19, alternate embodiments of thetransmitter-receiver 82 are contemplated. For example, one or more ofthe alternate embodiments described above in conjunction with thetransmitter-receiver 82 of FIG. 18 can apply to the transmitter-receiver82 of FIG. 19. Furthermore, the transmitter-receiver 82 of FIG. 19 caninclude more than one concentric or adjacent circular array 180, or caninclude one or more additional arrays of another shape such as a square,rectangle, or triangle. For example, where the transmitter-receiver 82includes concentric circular arrays 180, the antennas 92 of the circulararrays may be aligned along the same radii or may be offset from oneanother in a circumferential direction. Or where thetransmitter-receiver 82 includes three or more concentric circulararrays 180, the radial spacing between antennas in one array andantennas in another array can be uniform or non-uniform, and can begreater than, equal to, or less than

$\frac{\lambda_{c}}{2}.$

If this radial spacing is greater than or equal to

$\frac{\lambda_{c}}{2},$

then the circumferential spacing between at least two of the antennas 92is less than

$\frac{\lambda_{c}}{2}$

so as to provide a channel capacity C that is greater than thesaturation channel capacity C_(saturation).

FIG. 20 is a diagram of the MIMO-OFDM transmitter-receiver 82 of FIG. 7,according to another embodiment where the antennas 92 are configured toprovide a channel capacity C that exceeds the saturation channelcapacity C_(saturation), and where like numbers reference items commonto FIGS. 12 and 20, it being understood that the antennas 94 of theMIMO-OFDM transmitter-receiver 84 of FIG. 7 can be configured similarly.

The transmitter-receiver 82 includes mT antennas 92 ₀-92 _(mT-1), whichare configured in a three-dimensional array 190 having m layers 192₀-192 _(m-1). Adjacent ones of the antennas 92 are separated by auniform minimum distance

$d_{6} < {\frac{\lambda_{c}}{2}.}$

The distance d₆ may be measured from an edge of an antenna 92 to an edgeof an adjacent antenna 92, or, may be measured between the geometricalcenters, the centers of mass, the center axes, or other suitable pointsof the adjacent antennas 92.

The antennas 92 can have radiation patterns, directivities,orientations, and other characteristics according to any of theembodiments described above in conjunction with FIGS. 12-17, or may haveother radiation patterns, directivities, orientations, orcharacteristics as long as the antennas 92 present to other MIMO-OFDMtransmitter-receivers antenna profiles that sufficiently diversify thechannel so that the channel capacity C is greater a saturation capacityC_(saturation) of the channel. For example, the antennas 92 can eachhave a same radiation pattern, same directivity, a same orientation, andsame other characteristics relative to a line (e.g., a row, a column, ora layer line) along which the antenna lies. Or one or more of theantennas 92 can each have a different (e.g., randomly generated)radiation pattern, directivity, orientation, or other characteristicsrelative to a line along which the antenna lies.

Still referring to FIG. 20, alternate embodiments of thetransmitter-receiver 82 are contemplated. For example, one or more ofthe alternate embodiments described above in conjunction with thetransmitter-receiver 82 of FIGS. 18-19 can apply to thetransmitter-receiver 82 of FIG. 20. Furthermore, although shown having arectangular shape, the array 190 can have any other suitablethree-dimensional shape such as a cylinder, sphere, cone, or horn.

FIG. 21 is a diagram of the MIMO-OFDM transmitter-receiver 82 of FIG. 7,according to another embodiment where the antennas 92 are configured toprovide a channel capacity C that exceeds the saturation channelcapacity C_(saturation), and where like numbers refer to like itemsrelative to FIG. 12, it being understood that the antennas 94 of theMIMO-OFDM transmitter-receiver 84 of FIG. 7 can be arranged similarly.

The transmitter-receiver 82 includes o triangular subarrays 200 of Tantennas 92, where the minimum spacing d₇ between subarrays is greaterthan or equal to

$\frac{\lambda_{c}}{2},$

and where the minimum spacing between the antennas within each subarrayis less man

$\frac{\lambda_{c}}{2}.$

The distance d₇ may be measured from an edge of a subarray 200 to anedge of an adjacent subarray, or, may be measured between thegeometrical centers, the centers of mass, the center axes, or othersuitable points of the adjacent subarrays; and the distances between theantennas within the subarrays 200 can be measured similarly.Furthermore, an edge of a subarray 200 may be along a curve thatconnects the outermost antennas 92 in the subarray, or a curve thatencloses all of the antennas in the subarray.

Consequently, if, in a particular configuration or application theantennas 92 within each subarray 200 are too close together to furtherdiversify a channel (e.g., when a receiver is in the far field of thetransmitter-receiver 82), then the transmitter-receiver 82 can use asingle antenna from each subarray to transmit a respective data symbolDS (or multiple antennas within each subarray to transmit a same datasymbol DS).

The antennas 92 within each subarray 200 may have radiation patterns,directivities, orientations, or other characteristics according to anyof the embodiments described above in conjunction with FIGS. 12-17, ormay have other radiation patterns, directivities, orientations, andcharacteristics as long the antennas present to another MIMO-OFDMtransmitter-receiver antenna profiles that sufficiently diversify thechannel so that the channel capacity C is greater a saturation capacityC_(saturation) of the channel.

Still referring to FIG. 21, alternate embodiments of thetransmitter-receiver 82 are contemplated. For example, although thesubarrays 200 of antennas 92 are described as being two-dimensional andhaving equilateral-triangular shapes, the subarrays may beone-dimensional or three-dimensional, may have any suitable shapes, andmay have different sizes. Furthermore, although each subarray 200 isdescribed as including the same number T of antennas 92, one or moresubarrays may have a different number of antennas relative to the othersubarrays. In addition, although described as being uniformly spacedfrom one another, the subarrays 200 may be non-uniformly spaced from oneanother.

Described below in conjunction with FIGS. 22-37 are antennas that can beused as the antennas 92 and 94 of FIGS. 7-21 and the radiation patternsof these antennas, according to embodiments.

FIG. 22 is a diagram of a half-wave dipole antenna 210, which can beused as one or more of the antennas 92 and 94 of the MIMO-OFDMtransmitter-receivers 82 and 84 of FIGS. 7-21, according to anembodiment.

The antenna 210 is made of conductor 212, such as copper, which has a

${diameter}\text{/}{thickness}{{\operatorname{<<}\frac{\lambda_{c}}{2}}.}$

The conductor 212 includes two portions 214 and 216. The portion 214 hasa drive end 218 and a termination end 220, and the portion 216 has adrive end 222 and a termination end 224. The drive ends 218 and 222 arein the center of the antenna 210 (i.e., the antenna is a center-tappedhalf-wave dipole antenna) and are relatively close together such thatthe combined length l of the antenna along its axis 226 is equal to

$\frac{\lambda_{c}}{2};$

alternatively, l may be slightly less than

$\frac{\lambda_{c}}{2}$

to reduce the reactive portion of the antenna's impedance to, or near,zero. Furthermore, the directivity D of the antenna 210 is, or isapproximately, 1.76 dBi if the antenna operates other f_(c)(non-resonant dipole), and is, or is approximately, 2.15 dBi if theantenna operates at f_(c) (resonant dipole), and the electric field ofthe electromagnetic waves that the antenna emits are linearly polarizedin the dimension of the axis 226.

In operation during signal transmission, the transmitter-receivercircuitry 88 or 90 (FIGS. 7-21) drives the drive ends 218 and 222differentially with a MIMO-OFDM signal, and during signal reception thetransmitter-receiver circuitry differentially receives a MIMO-OFDMsignal via the drive ends 218 and 222.

FIG. 23 is a diagram of the radiation pattern 230 of the half-wavedipole antenna 210 of FIG. 22, according to an embodiment.

Although in each horizontal plane that is perpendicular to the antennaaxis 226 the antenna 210 has an omnidirectional radiation pattern, theantenna 210, when used as one or more of the antennas 92 and 94 of FIGS.7-21, can still be used to diversify the communication channel. Forexample, the axes 226 of two or more of the antennas 210 may be orientedin different directions (i.e., nonparallel to one another), so that in asame plane the antennas present different gains or polarizations.Alternatively, two or more of the antennas 210 may be located atdifferent heights above a reference plane even if their axes 226 areparallel to one another so that in a same plane the antennas presentdifferent gains or polarizations.

Referring to FIGS. 22-23, alternate embodiments of the antenna 210 arecontemplated. For example, to allow densely arranging the antennas 92and 94 of the MIMO-OFDM transmitter-receivers 82 and 84 of FIG. 7 with aminimum antenna spacing of less than, even much less than,

$\frac{\lambda_{c}}{2},$

one can modify the antenna 210 such that its length

$l < {\frac{\lambda_{c}}{2}.}$

One can even modify the antenna 210 such that its length

${l{\operatorname{<<}\frac{\lambda_{c}}{2}}},$

in which case the antenna is considered to be deeply subwavelength. Andto further diversify the channel, one can increase the directivity D ofsuch a reduced-length version of the antenna 210 by increasing theantenna's Q-factor to ten, one hundred, or beyond according totechniques that are described below.

FIG. 24 is a diagram of a quarter-wave dipole antenna 240 with groundplane 242, which together can be used as one or more of the antennas 92and 94 of the MIMO-OFDM transmitter-receivers 82 and 84 of FIGS. 7-21,according to an embodiment.

The antenna 240 is similar to the resonant half-wave dipole 210 of FIG.22 except that it includes only the upper portion 216 of the conductor212 having a length

${l\text{/}2} = \frac{\lambda_{c}}{4}$

(or slightly less than this to reduce the reactive portion of theantenna's impedance to, or to near, zero). The ground plane 242, whichis sometimes called a redirector or reflector plane, is formed from aconductive material (e.g., copper) and redirects energy emitted by theantenna 240 such that on the same side of the ground plane as theantenna, the antenna appears as a half-wavelength dipole antenna. Andthe distance d₈ between the drive end 222 and the ground plane 242 istypically much less than l/2.

In operation during signal transmission, the transmitter-receivercircuitry 86 or 88 (FIGS. 7-21) drives the drive end 222 in asingle-ended manner with a MIMO-OFDM signal, and during signal receptionthe transmitter-receiver circuitry receives, in a single-ended manner, aMIMO-OFDM signal via the drive end 222.

FIG. 25 is a diagram of the radiation pattern 250 of the quarter-wavedipole antenna 240 of FIG. 24, according to an embodiment.

Although in each horizontal plane that is perpendicular to the antennaaxis 226 the antenna 240 has an omnidirectional radiation pattern, theantenna 240, when used as one or more of the antennas 92 and 94 of FIGS.7-21, can still be used to diversify the communication channel. Forexample, the axes 226 of two or more of the antennas 240 and theirground planes 242 may be oriented in different directions (i.e.,nonparallel to one another), so that in a same plane the antennaspresent different gains or polarizations. Alternatively, two or more ofthe antennas 240 and their ground planes 242 may be located at differentheights above a reference plane even if their axes 226 are parallel toone another so that in a same plane the antennas present different gainsor polarizations.

Referring to FIGS. 24-25, alternate embodiments of the antenna 240 arecontemplated. For example, to allow densely arranging the antennas 92and 94 of the MIMO-OFDM transmitter-receivers 82 and 84 of FIG. 7 with aminimum spacing of less than, even much less than,

$\frac{\lambda_{c}}{2},$

one can modify the antenna 240 such that its length

${l\text{/}2} < {\frac{\lambda_{c}}{4}.}$

One can even modify the antenna 240 such that its length

${l\text{/}2{\operatorname{<<}\frac{\lambda_{c}}{2}}},$

in which case the antenna is considered to be deeply subwavelength. Andto further diversify the channel, one can increase the directivity D ofsuch a reduced-length version of the antenna 240 by increasing theantenna's Q-factor to ten, one hundred, or beyond according totechniques that are described below.

FIG. 26 is a diagram of a polarized antenna 252, which can be used asone or more of the antennas 92 and 94 of the MIMO-OFDMtransmitter-receivers 82 and 84 of FIGS. 7-21, according to anembodiment.

The antenna 252 is made of two half-wavelength dipoles 254 and 256, eachof which may be the same as, or similar to, the half-wavelength dipole210 of FIG. 22, and which are oriented perpendicular to one another.

One may alter the polarization pattern of the antenna 252 in a number ofdifferent ways. For example, one may vary the polarization pattern byvarying the phase difference between the signals transmitted or receivedby the antenna. Furthermore, one may change the angle (90° as shown)between the two dipoles 254 and 256. In addition, one may arrange thedipoles 254 and 256 so that their centers do not coincide; for example,sliding the dipole 256 to the right results in the portion of the dipole256 to the left of the dipole 254 to be shorter than the portion of thedipole 256 to the right of the dipole 254.

FIGS. 27-28 are plan-view and side-view diagrams, respectively, of apatch antenna 260, which can be used as one or more of the antennas 92and 94 of the MIMO-OFDM transmitter-receivers 82 and 84 of FIGS. 7-21,according to an embodiment.

The antenna 260 includes a plate, i.e., patch 262, made from aconductive material, such as copper, which has a thickness

$T_{h\; 1}{\operatorname{<<}\frac{\lambda_{c}}{2}}$

and which has a length

$l = \frac{\lambda_{c}}{2}$

and a width w, where w=l in the described embodiment. A microstrip 264feeds the MIMO-OFDM signal from the transmitter-receiver circuitry 88 or90 (FIGS. 7-21) to the patch 262 such that the electric fields of theelectromagnetic waves generated by the patch antenna 260 are linearlypolarized in the 1 dimension.

The patch 262 is disposed over a ground plane 266, which is also madefrom a conductive material such as copper and which has, for example,the same thickness T_(h1) as the patch. Typically, the ground plane 266has the same shape as, but is larger than, the patch 262 in one or bothof the length and width dimensions, and one can alter the radiationpattern (see FIG. 29 below) of the antenna 260 by varying the size ofthe ground plane in one or both of the length and width dimensions.

An insulating separation layer 268 made, for example, from a dielectricmaterial such a printed circuit board (PCB), is disposed between thepatch 262 and the ground plane 266. The layer 268 has a thicknessT_(h2), where

${T_{h\; 1} < {T_{h\; 2}{\operatorname{<<}\frac{\lambda_{c}}{2}}}},$

where the impedance, Q, and bandwidth of the antenna 260 are dependenton T_(h2). That is, a designer can adjust T_(h2) to vary one or more ofthe impedance, Q, and bandwidth of the antenna 260.

A radome 270, which is made from a nonconductive material such as aplastic, forms a protective covering over the patch 262, microstrip 264,ground plane 266, and separation layer 268.

The antenna 260 can also include a conventional cable connector (e.g.,coaxial cable) 272 having a signal conductor coupled to the microstrip264 and a ground conductor coupled to the ground plane 266. The cableconnector 272 can allow one to couple the patch antenna 260 to thetransmitter-receiver circuitry 88 or 90 (FIGS. 7-21) via a conventionalcable (e.g., a coaxial cable).

FIG. 29 is a diagram of the radiation pattern 280 of the patch antenna260 of FIGS. 27-28, according to an embodiment. The pattern 280 is in aplane that is normal to the surface of the patch 262 and that isparallel to the length l dimension of the patch, and the directivity Dof the patch antenna 260 is approximately 9 dBi.

In an embodiment, the radiation pattern (not shown in FIG. 28) in aplane that is normal to the surface of the patch 262 and that isparallel to the width w dimension of the patch may be similar to theradiation pattern 280.

Referring to FIGS. 27-29, alternate embodiments of the patch antenna 260are contemplated. For example, the separation layer 268 may be a gapfilled with a fluid such as air. Furthermore, one can alter themicrostrip 264, or add slots to the patch 262, in a conventional mannersuch that the antenna 260 produces circularly polarized waves instead oflinearly polarized waves. Moreover, to allow densely arranging theantennas 92 and 94 of the MIMO-OFDM transmitter-receivers 82 and 84 ofFIGS. 7-21 with a minimum spacing of less than, even much less than,

$\frac{\lambda_{c}}{2},$

one can modify the antenna 260 such that its length l and width w areboth less than

$\frac{\lambda_{c}}{2}.$

One can even modify the antenna 260 such that its length l and width ware much, much less than

$\frac{\lambda_{c}}{2},$

in which case the antenna is considered to be deeply subwavelength. Inaddition, the ground plane 266 can be a metamaterial surface such asdescribed below in conjunction with FIGS. 31-33. And to furtherdiversify the channel, one can increase the directivity D of such areduced-area version of the antenna 260 by increasing the antenna'sQ-factor to ten, one hundred, or beyond according to techniques that aredescribed below.

FIG. 30 is diagram of a multiple-element antenna 290, which can be usedas one or more of the antennas 92 and 94 of the MIMO-OFDMtransmitter-receivers 82 and 84 of FIGS. 7-21, according to anembodiment.

The antenna 290 includes multiple antenna elements 292, which areseparated by a uniform distance

${e_{l}{\operatorname{<<}\frac{\lambda_{c}}{2}}},$

where e can be measured between, for example, the edges, geometriccenters, central axes, or centers of mass of adjacent antenna elements292. By selectively activating and deactivating one or more of theelements 292, the transmitter-receiver circuitry 88 or 90 (FIGS. 7-21)can alter one or more characteristics (e.g., radiation pattern,directivity, gain, phase, polarization) of the antenna 290, and,therefore, can tailor the transmission or the reception profile that theantenna presents to another MIMO-OFDM transmitter-receiver. And thisaltering and tailoring can be performed and fixed one time by themanufacturer or user, or the MIMO-OFDM transmitter-receiver 82 or 84 canperform this altering and tailoring dynamically depending on the channelconditions so as to increase the capacity of the channel above thechannel's saturation capacity, and even to maximize the channel capacity(altering the transmission characteristics of an antenna is describedfurther below in conjunction with FIG. 41).

Each element 292 of the antenna 290 may itself be an antenna such as ahalf-wave dipole, may be a nonconductive element such as a dielectric,may be a conductive element, or may be a metamaterial element asdescribed below in conjunction with FIGS. 31-33.

To deactivate an element 292, the transmitter-receiver circuitry 88 or90 (FIGS. 7-21) can electrically uncouple the element from all voltagereferences such that the element floats electrically.

To activate an element 292 while the transmitter-receiver circuitry 88or 90 (FIGS. 7-21) is transmitting a signal via the antenna 290, thetransmitter-receiver circuitry can couple the element to a fixed voltagereference (e.g., ground or a non-zero voltage), can drive the elementwith the MIMO-OFDM signal being transmitted, or can drive the elementwith another signal such as a phase-shifted or gain-altered version ofthe MIMO-OFDM signal being transmitted.

To activate an element 292 while the transmitter-receiver circuitry 88or 90 (FIGS. 7-21) is receiving a signal via the antenna 290, thetransmitter-receiver circuitry can couple the element to a fixed voltagereference, can couple the element to a time-varying voltage, can couplethe element to the transmitter-receiver circuitry with no phase shift orattenuation/amplification, or can couple the element to thetransmitter-receiver circuitry via a phase shifter orattenuator/amplifier.

Still referring to FIG. 30, alternate embodiments of the antenna 290 arecontemplated. For example, although the antenna elements 292 aredescribed as being arranged along a straight line in one dimension, theelements may be arranged in two or three dimensions and in any suitableshape (e.g., rectangle, square, circle, triangle, cube, sphere,cylinder, cone, or horn). Furthermore, although described as beingspaced apart by a uniform distance e₁, two or more of the elements 292may be spaced apart by different distances that are less than

$\frac{\lambda_{c}}{2}.$

Moreover, to allow densely arranging the antennas 92 and 94 of theMIMO-OFDM transmitter-receivers 82 and 84 of FIGS. 7-21 with a minimumspacing of less than, even much less than,

$\frac{\lambda_{c}}{2},$

one can modify the antenna 290 such that its length

$l < {\frac{\lambda_{c}}{2}.}$

One can even modify the antenna 290 such that its length

${l{\operatorname{<<}\frac{\lambda_{c}}{2}}},$

in which case the antenna is considered to be deeply subwavelength. Andto further diversify the channel, one can increase the directivity D ofsuch a reduced-length version of the antenna 290 by increasing theantenna's Q-factor to ten, one hundred, or beyond according totechniques that are described below.

FIGS. 31-33 are plan-view, side-view, and magnified plan-view diagrams,respectively, of a metamaterial antenna 300, which can be used as one ormore of the antennas 92 and 94 of the MIMO-OFDM transmitter-receivers 82and 84 of FIGS. 7-21, according to an embodiment.

The antenna 300 includes a base 302 formed from a nonconductive materialsuch as a dielectric, a waveguide plate 304 formed from a conductivematerial such as copper, metamaterial elements 306 disposed over theplate, each element separated from adjacent elements by a uniformdistance

${e_{2}{\operatorname{<<}\frac{\lambda_{c}}{2}}},$

and a signal coupler 308. The elements 306 may be conductive,nonconductive, or may be separated from the waveguide plate 304 by athin nonconductive, electrically insulating layer (not shown in FIGS.31-33). Together, the base 302, plate 304, and elements 306 form ametamaterial; that is, neither the base, plate, nor elements alone forma metamaterial, but the combination of these items forms a metamaterial.Furthermore, the plate 304 and the elements 306 form a metamaterialsurface 310.

The diameter da₂ of the antenna 300 is greater than or equal to

$\frac{\lambda_{c}}{2},$

and the thickness T_(h3) of the waveguide plate 304 is

${\operatorname{<<}\frac{\lambda_{c}}{2}}.$

The thickness T_(h4) of the base 302 can be any thickness that issuitable for providing sufficient support and stability to the antenna300, and the thickness T_(h4) and the other electromagnetic propertiesof the base 302 can be any values suitable to provide acceptableboundary conditions between the base and the plate 304 for a particularapplication.

By selectively activating and deactivating one or more of themetamaterial elements 306 (this activating and deactivating may be donevia the connector 308 or via another connector not shown in FIGS.31-33), the transmitter-receiver circuitry 88 or 90 (FIGS. 7-21) canalter one or more characteristics (e.g., radiation pattern, directivity,gain, phase, polarization) of the antenna 300, and, therefore, cantailor the transmission profile or the reception profile that theantenna presents to another MIMO-OFDM transmitter-receiver. And thisaltering and tailoring can be performed and fixed one time by themanufacturer or user, or the MIMO-OFDM transmitter-receiver 82 or 84(FIGS. 7-21) can perform this altering and tailoring dynamicallydepending on the channel conditions so as to increase the capacity ofthe channel above the channel's saturation capacity, and even tomaximize the channel capacity.

To deactivate an element 306, the transmitter-receiver circuitry 88 or90 (FIGS. 7-21) may electrically uncouple the element from all voltagereferences such that the element floats electrically.

To activate an element 306 while the transmitter-receiver circuitry 88or 90 (FIGS. 7-21) is transmitting or receiving a signal via the antenna300, the transmitter-receiver circuitry can couple the element to afixed voltage reference (e.g., ground, a nonzero voltage), can drive theelement with another signal such as an AC signal, or can couple theelement to the waveguide plate 304 such that the element is at the samevoltage potential as portion of the plate 304 that the element contacts.

In operation during a transmit mode, the transmit-receive circuitry 88or 90 (FIGS. 7-21) drives the waveguide plate 304 with the MIMO-OFDMsignal via the connector 308, causing a wave, such as a standing wave,to form in the waveguide plate.

According to known principles of refraction and diffraction, themetamaterial elements 306 cause the MIMO-OFDM signal to radiate from themetamaterial surface 310 with transmission characteristics (e.g.,radiation pattern, directivity, gain, phase, polarization) that are setby the pattern of active and inactive metamaterial elements. If thetransmitter-receiver circuitry 88 or 90 (FIGS. 7-21) can alter thispattern dynamically, then the transmitter-receiver circuitry candynamically alter one or more transmission characteristics of theantenna 300, and thus can dynamically alter the transmission profilethat the antenna presents to one or more receive antennas.

In operation during a receive mode, the metamaterial elements 306cooperate to couple an incoming MIMO-OFDM signal to the waveguide plate304, thus causing to form in the waveguide plate a wave, such as astanding wave, that propagates to the transmit-receive circuitry 88 or90 (FIGS. 7-21) via the connector 308.

According to known principles of refraction and diffraction, themetamaterial elements 306 couples to the waveguide plate 304 theMIMO-OFDM signal incident on the metamaterial surface 310 with receptioncharacteristics (e.g., radiation pattern, directivity, gain, phase,polarization) that are set by the pattern of active and inactivemetamaterial elements. If the transmitter-receiver circuitry 88 or 90(FIGS. 7-21) can alter this pattern dynamically, then thetransmitter-receiver circuitry can dynamically alter one or morereception characteristics of the antenna 300, and thus can dynamicallyalter the reception profile that the antenna presents to one or moretransmit antennas.

Still referring to FIGS. 31-33, alternate embodiments of the antenna 300are contemplated. For example, although the antenna elements 306 aredescribed as being arranged in a circular two-dimensional array, theelements may be arranged in one or three dimensions and in any suitableshape (e.g., rectangle, square, triangle, cube, sphere, cylinder, cone,horn). Furthermore, although described as being spaced apart by anuniform distance e₂, two or more of the elements 306 may be spaced apartby different distances that are less than

$\frac{\lambda_{c}}{2}.$

Moreover, although e₂ is described as being measured between edges ofadjacent elements 306, e₂ may be measured between the geometricalcenters, the centers of mass, the central axes, or other points of theadjacent antenna elements. In addition, although the diameter da₂ of theantenna 300 is described as being greater than or equal to

$\frac{\lambda_{c}}{2},$

da₂ may be less than, even much, much less than,

$\frac{\lambda_{c}}{2}.$

Furthermore, the metamaterial elements 306 may be arranged such thatthey, together with the waveguide plate 304 and the base 302, can formmultiple antennas 300; for example, the metamaterial elements, waveguideplate, and base may form all of antennas 92 of the transmitter-receiver82 (FIGS. 7-21) or all of the antennas 94 of the transmitter-receiver 84(FIGS. 7-21).

FIGS. 34-37 are diagrams of metamaterial elements that can be used asone or more of the metamaterial elements 306 of FIGS. 31-33, accordingto an embodiment.

FIG. 34 is a diagram of a conventional split-ring resonator 320, whichmay form, or form a part of, one or more of the metamaterials elements306 of FIGS. 31-33, according to an embodiment; the resonator 320 mayalso be called an electrical inductor-capacitor element. The resonator320 includes split-ring elements 322 and 324, which are formed from aconductive material, such as copper, and which have respective gaps 326and 328. A nonconductive fluid such as air or a solid dielectric mayfill the gaps 326 and 328. And the dimensions of the resonator 320 areall

${\operatorname{<<}\frac{\lambda_{c}}{2}}.$

Furthermore, although shown as being round, the split-ring elements 322and 324 may have any suitable shape such as square, rectangular, ortriangular.

FIG. 35 is a diagram of a conventional open split-ring resonator 340,which may form, or form a part of, one or more of the metamaterialselements 306 of FIGS. 31-33, according to an embodiment; the resonator340 may also be called an electrical inductor-capacitor element. Theresonator 340 includes split-ring elements 342 and 344, which are formedfrom a conductive material, such as copper, and which have respectivegaps 346 and 348. A nonconductive fluid such as air or a soliddielectric may fill the gaps 346 and 348. And the dimensions of theresonator 340 are all

${\operatorname{<<}\frac{\lambda_{c}}{2}}.$

Furthermore, although shown as being round, the split-ring elements 342and 344 may have any suitable shape such as square, rectangular, ortriangular.

FIG. 36 is a diagram of a conventional complementary split-ringresonator 360, which may form, or form a part of, one or more of themetamaterials elements 306 of FIGS. 31-33, according to an embodiment;the resonator 360 may also be called a complementary electricalinductor-capacitor element. The resonator 360 includes a resonator plate362, which is formed from a conductive material, such as copper, andwhich has split-ring gaps 364 and 366 formed therein. A nonconductivefluid such as air or a solid dielectric may fill the gaps 364 and 366.And the dimensions of the resonator 360 are all

${\operatorname{<<}\frac{\lambda_{c}}{2}}.$

Furthermore, although described as being round, the split-ring gap 364may have any suitable shape such as square, rectangular, or triangular.Moreover, although described as being candy-cane shaped, the split-ringgap 366 may have any suitable shape such as an “L” shape or an arrowshape.

FIG. 37 is a diagram of a conventional electrical inductor-capacitorelement 380, which may form, or form a part of, one or more of themetamaterials elements 306 of FIGS. 31-33, according to an embodiment.

The electrical inductor-capacitor element 380 includes a capacitor 382having a first capacitor plate 384 and a second capacitor plate 386. Thefirst capacitor plate 384 is formed from a conductive material, such ascopper, and has fingers 388; likewise, the second capacitor plate 386 isformed form a conductive material, such as copper, and includes fingers390 that are interleaved with the fingers 388. A nonconductive fluidsuch as air or a solid dielectric can fill gaps 392 between the fingers388 and 390. The element 380 also includes an inductor 394 formed from aconductive material, such as copper, and a nonconductive fluid such asair or a solid dielectric can fill gaps 396 between the windings of theinductor. A strip 398, which is formed from a conductive material suchas copper, electrically and structurally couples together, and isintegral with, the second capacitor plate 386 and the inductor 394.Although described as being a straight parallel-plate capacitor, thecapacitor 382 can have any suitable shape; likewise, although describedas having a square shape, the inductor 394 can have any suitable shapesuch as round. And the dimensions of the element 380 are all

${\operatorname{<<}\frac{\lambda_{c}}{2}}.$

Referring again to FIGS. 7 and 12-33, it is evident that antennas havinghigh directivities D can be used as the antennas 92 and 94 to diversifythe communication channel sufficiently to provide a channel capacity Cthat exceeds the saturation channel capacity C_(saturation).

In a densely packed (minimum spacing substantially less than

$\left. \frac{\lambda_{c}}{2} \right)$

array of antennas, the antennas, and, therefore, the elements that formmulti-element antennas, can be deeply subwavelength in their dimensions(e.g., length, width, depth/thickness, diameter); as such they can beclassified as electrically small antennas, with a nuance discussedbelow.

The maximum directivity D of electrically small antennas, in particular,the fundamental limits thereupon, has been the subject of many studiesin the past. For example, an electrically small dipole already has anon-negligible directivity of D=1.50 (1.76 dBi). Per FIGS. 22-23, thisdirectivity alone can have a non-negligible effect on the capacity of aMIMO-OFDM communication channel. And an ideal half-wave (“resonant”)dipole has an even higher directivity D=1.64 (2.15 dBi).

Theoretical considerations suggest that the so-called normal directivityD, i.e., the maximum directivity D achievable in a non-resonant antenna(antennas with a resonance Q-factor on the order of unity or belowunity) is approximately D_(max)=AP²+2AP, where AP (a dimensionlessaperture parameter)=max(1, k₀Ra), k₀ is the free-space wavenumber (notto be confused with a k subcarrier), and Ra is the antenna radius (halfof its diameter). Another theory suggests that the upper limit fornormal directivity is D_(max)=AP²+2AP+1=(AP+1)². The AP parametersignifies the highest order of a spherical harmonic (or multipole) whichcan efficiently interact with the antenna of that radius. For anelectrically small antenna, AP=1, because the dipole harmonic alwaysexists. In either case, the directivity D of electrically small andnon-resonant antennas is capped at 3−4 (4.8−6.0 dBi) according to thesetheories.

A patch (microstrip) antenna, such as described above in conjunctionwith FIGS. 27-29 has a substantially higher directivity D in the range3.2-6.3 (5-9 dBi); however, its unusual directivity is actually due tothe participation of the conducting ground plane or dielectricsubstrate. Currents induced in the ground plane or substrate contributeto the radiation pattern and lead to an effective increase in the sizeof the patch effective aperture.

This observation leads to a range of embodiments for highly-directive,deeply subwavelength, antennas and antenna elements. Certain antennageometries, such as those used in metamaterial antennas, such asdescribed above in conjunction with FIGS. 31-33, utilize a ground planeand a one-dimensional or two-dimensional array of antenna elements aboveit. While the directivity D of any such element without the ground planeand in free space is rather low, and limited by the “normal directivity”theories to a value of 3-6 dBi as described above, in combination with avery wide ground plane these elements can have individual directivitiesreaching 8-9 dBi, with no known fundamental limit. Such antenna elementscan be, for example, rectangular patches (as in the classical patchantenna such as described above in conjunction with FIGS. 27-29), orthey can have more intricate shapes, like split-ring resonators (SRR),electrical-inductor-capacitor (ELC) elements and their complementaryversions (cSRR, cELC) such as described above in conjunction with FIGS.34-37. The ground plane itself may be a simple electrical conductor, ora patterned “metasurface” (such as the metasurface 310 described abovein conjunction with FIGS. 31-33) exhibiting a wide range of surfaceimpedances, including the known high-impedance (“magnetic ground plane”)limit.

Furthermore, interactions between densely packed, tightly spacedantennas or antenna elements can lead to an increase in the effectiveaperture of each antenna/element, which can enable a higher-than-normaldirectivity D for each antenna/element. In such a mode of operation, thesurrounding antennas/elements act as passive, parasiticantennas/elements each having an impedance that can be tuned tofacilitate the creation of a desirable individual-element radiationpattern and directivity.

In such a configuration, it is worth noting that, although multipleantennas/elements participate simultaneously in sending or receiving asignal, the degrees of freedom are nevertheless not lost by virtue ofdilution because each multi-antenna/multi-element excitation patternstill has a well-defined power peak with a unique transverse coordinate(this power peak is typically adjacent to the active antenna/elementthat is being excited). As long as the radiation patterns created byfeeding one antenna/element at a time are all distinguishable at thereceiver antenna array, these patterns count as linearly independentdegrees of freedom (i.e., correspond to linearly independentrows/columns of the estimated channel matrix). In general, the effectiverank of the estimated channel matrix is not affected by the mutualcoupling between the elements, with the exception of special cases wherethis coupling is purposely designed to create linear dependenciesbetween the excitation vectors (such special cases are typically notuseful to increase the channel capacity by increasing the channeldiversity).

A further increase in the directivity D of individual antennas orantenna elements can be obtained when these antennas/elements are highlyresonant, that is, when they are characterized by a high Q factor(Q>>1). The normal directivity D described above applies to a situationwhere the antenna Q-factor is kept low (e.g., on the order of unity).When no constraint is placed on the Q-factor of the antenna/element(and, consequently, the modal Q-factors corresponding to variousspherical harmonics are also unlimited), it has been shown by numerousindependent studies that the antenna directivity D is not at all limitedby any dimensional parameter such as the free-space wavelength. In otherwords, arbitrarily high-Q antennas can be arbitrarily directive,regardless of their size relative to the wavelength. Antennas havingdirectivity D or gain in excess of the “normal gain” are known assuperdirective or supergain antennas.

In general, a low Q-factor can be a desirable feature of a conventionalcommunications antenna/element as it enables wide InstantaneousBandwidth (IBW). For this reason, super-gain antennas/elements are oftendeemed impractical for communications. However, in certain applicationssuch as MIMO-OFDM, the available bandwidth is pre-allocated (forexample, as a licensed band in the regulated portion of the spectrum).In such applications, the pre-allocated bandwidth can be rather small—onthe order of 1% of the MIMO-OFDM carrier frequency f_(c). This impliesthat a relatively high-Q antenna (with Q>1, such as Q˜10 or higher, orQ˜100 or higher) can utilize the entire pre-allocated band efficientlyas the band fits within its IBW.

Q-factors in the range of hundreds are readily achievable with regularmetals at room temperatures and microwave frequencies; a metamaterialantenna with metamaterial-forming antenna elements is an example. Whilemost metamaterial resonators considered are small electrical or magneticdipoles, all of the above techniques can utilize higher-order multipoleantenna elements as well.

With superconducting metals at temperatures below their superconductingtransition, the Q-factors are virtually unlimited. As radiationimpedance is the only source of resonator decay rate, the Q-factors canbe driven higher by suppressing the radiation impedance throughlow-order multipole moments. By increasing the internal structuralcomplexity, ohmic loss-free resonators can be turned into arbitrarilyhigh-order multipoles, whose radiative decay rate scales as a power lawwith the minimum order of the radiating multipole.

In summary, antennas and antenna elements, such as the antenna andantenna elements described above in conjunction with FIGS. 12-37, can bemade to have higher directivities D by increasing their Q-factors asdescribed immediately above. And, as described above in conjunction withFIGS. 7 and 12-33, using antennas with relatively high directivities Din a MIMO-OFDM transmitter-receiver, such as the transmitter-receivers82 and 84 of FIGS. 7 and 12-21, can increase the channel capacity Cbeyond the saturation capacity C_(saturation) by increasing thediversity of the channel.

FIG. 38 is a flow diagram of a procedure 400, which the MIMO-OFDMtransmitter-receiver 82 of FIGS. 7 and 12-21 can use to determine howmany respective data symbols that it can transmit simultaneously to theMIMO-OFDM transmitter-receiver 84, according to an embodiment. Althoughthe transmitter-receiver 82 is described as transmitting data symbols tothe transmitter-receiver 84, it is understood that a description of thetransmitter-receiver 84 transmitting data symbols to thetransmitter-receiver 82 would be similar. Furthermore, for purposes ofexample, in the below example the transmitter-receiver 82 is referred toas the transmitter, and the transmitter-receiver 84 is referred to asthe receiver. Moreover, for purposes of example, it is assumed that theconfigurations of the antennas 92 and 94 are fixed, and were determinedpreviously to be suitable for increasing the channel diversity in theparticular environment (e.g., home, office, public area) in which thetransmitter 82 and receiver 84 are being used. In addition, although anaction may be attributed to the transmitter 82 or the receiver 84, it isunderstood that such action is performed by circuitry on board thetransmitter or receiver, such as the transmitter circuitry 100 of FIG.8, the receiver circuitry 120 of FIG. 9, other circuitry that is part ofthe transmitter-receiver circuitry 88 or 90 of FIGS. 7 and 12-21, orother circuitry that is part of the transmitter 82 or the receiver 84.

First, at a step 402, the transmitter 82 determines the distance betweenthe transmitter 82 and the receiver 84. The transmitter 82 may do thisusing any suitable conventional distance-determining technique.

Next, at a step 404, the transmitter 82 determines whether the receiver84 is within the near field of the transmitter 82. Although the boundarybetween the near field and far field of the aperture formed by thetransmit antennas 92 can be difficult to calculate precisely, e.g.,because the boundary depends on the number and location of scatteringobjects in the subchannel portions between the transmitter 82 andreceiver 84, one can calculate, a priori, a conservative boundary basedon the configuration of the antennas 92, the configuration of theantennas 94 (if known a priori), and the statistical channel state forthe particular application or environment in which the transmitter 82and receiver 84 are being used. For example, one can calculatenear-field/far-field boundaries for different applications andenvironments, store them in a look-up table (LUT, not shown in FIG. 7,12-21, or 38), and use as the boundary the stored boundary value thatcorresponds most closely with the current application or environment,which one may input to the transmitter 82 during its set up (e.g., inresponse to a set-up wizard or the like).

If the transmitter 82 determines that the receiver 84 is in the nearfield of the transmitter 82, then, at a step 406, the transmitter 82transmits training symbols from each of the transmit antennas 92 so thatthe receiver 84 can estimate the channel matrix Ĥ. Then, the transmitter82 transmits a respective data symbol via each of the transmit antennas92. That is, the transmitter 82 “assumes” that because the receiver 84is within the transmitter's near field, the channel is sufficientlydiverse for the receiver to distinguish all of the transmit antennas 92.Consequently, because the minimum spacing between adjacent transmitantennas 92 is less than

$\frac{\lambda_{c}}{2}$

and the receiver 84 is within the near field of the transmitter 82, thetransmitter is able to take advantage of the channel capacity providedby the transmit antennas, which capacity is above the channel'ssaturation capacity.

In contrast, if the transmitter 82 determines that the receiver 84 isnot in the near field of the transmitter 82, then, at a step 408, thetransmitter 82 transmits training symbols only via ones of the transmitantennas 92 that are spaced apart by at least

$\frac{\lambda_{c}}{2}$

so that the receiver 84 can estimate the channel matrix Ĥ. Next, thetransmitter 82 transmits a respective data symbol only via the same onesof the transmit antennas 92 that are spaced apart by at least

$\frac{\lambda_{c}}{2}.$

For example, if the antennas 92 are arranged in subarrays 200 asdescribed above in conjunction with FIG. 21, then the transmitter 82transmits a single respective data symbol via the antennas in eachsubarray. The transmitter 82 can use a single antenna 92 within eachsubarray 200, or can use multiple antennas within each subarray totransmit the same respective data symbol so as to increase the SNR ofthe signal carrying this data symbol at the receiver 84. In thisexample, the transmitter 82 “assumes” that because the receiver 84 isnot within the transmitter's near field, the channel is insufficientlydiverse for the receiver to distinguish all of the transmit antennas 92,but is sufficiently diverse for the receiver to distinguish the transmitantennas that are spaced apart by at least

$\frac{\lambda_{c}}{2}.$

Consequently, the transmitter 82 “assumes' that in this situation, thechannel capacity is no more than its saturation capacity.

Still referring to FIG. 38, alternate embodiments of the procedure 400are contemplated. For example, the procedure 400 may include steps notdescribed herein, the procedure may omit one or more of the describedsteps, and the transmitter 82 may perform the steps 402-408 (minus anyomitted steps and including any added steps) in an order that isdifferent from the described order.

FIG. 39 is a flow diagram of a procedure 420, which the MIMO-OFDMtransmitter-receiver 84 of FIGS. 7 and 12-21 can use to determine howmany respective data symbols the MIMO-OFDM transmitter-receiver 82 (alsoof FIGS. 7 and 12-21) can transmit simultaneously to thetransmit-receiver 84, according to an embodiment. Although thetransmitter-receiver 82 is described as transmitting symbols to thetransmitter-receiver 84, it is understood that a description of thetransmitter-receiver 84 transmitting symbols to the transmitter-receiver82 would be similar. Furthermore, for purposes of example, in the belowexample the transmitter-receiver 82 is referred to as the transmitter,and the transmitter-receiver 84 is referred to as the receiver.Moreover, for purposes of example, it is assumed that the configurationsof the antennas 92 and 93 are fixed, and were determined previously tobe suitable for increasing the channel diversity in the particularenvironment (e.g., home, office, public area) in which thetransmitter-receivers 82 and 84 are being used. In addition, although anaction may be attributed to the transmitter 82 or the receiver 84, it isunderstood that such action is performed by circuitry on board thetransmitter or receiver, such as the transmitter circuitry 100 of FIG.8, the receiver circuitry 120 of FIG. 9, other circuitry that is part ofthe transmitter-receiver circuitry 88 or 90 of FIGS. 7 and 12-21, orother circuitry that is part of the transmitter 82 or the receiver 84.

First, at a step 422, the transmitter 82 transmits respective trainingsymbols from each of the antennas 92, where each of the training symbolsis different from the other training symbols. The transmitter 82 maytransmit each of the training symbols serially, i.e., at separate times,or may transmit the training symbols simultaneously such as describedabove in conjunction with FIGS. 3-4. Sending different training symbolshelps the receiver 84 better determine from which transmit antenna 92the transmitter 82 is transmitting each training symbol, particularlywhen the transmitter transmits the training symbols simultaneously.

Next, at a step 424, the receiver 84 estimates the channel matrix Ĥ.

Then, at a step 426, the receiver 84 determines whether the estimatedchannel matrix Ĥ is effectively full rank as described above inconjunction with FIG. 6.

If, at step 426, the receiver 84 determines that the channel is noteffectively full rank, then, at a step 428, the receiver identifies theone or more transmit antennas 92 that the receiver can distinguish; thatis, the receiver identifies the one or more transmit antennas that areassociated with rows/columns of the estimated channel matrix Ĥ that areeffectively linearly independent from the other rows/columns of Ĥ.

In contrast, if, at step 426, the receiver 84 determines that thechannel is effectively full rank, then, at a step 430, it identifies allof the transmit antennas 92 as being distinguishable at the receiver;that is, the receiver determines that all of the rows/columns of theestimated channel matrix Ĥ are effectively linearly independent from oneanother.

Next, at a step 432, for each signal pipe respectively associated withone of the identified transmit antennas 92, the receiver 84 determineswhether the gain of the signal pipe is sufficient to provide, at thereceiver, a SNR that is large enough for the receiver to recover asymbol from the MIMO-OFDM signal transmitted over the signal pipe. Forexample, the receiver 84 can determine whether a signal pipe hassufficient gain by calculating a sum Gain_(sum) of the gains over all ofthe subchannels 140 (FIGS. 7 and 12-21) that form the signal pipe (i.e.,all of the subchannels 140 associated with the transmit antenna 92corresponding to the signal pipe) and comparing this sum to a thresholdTh_(gain). If Gain_(sum)≧Th_(gain), then the receiver 84 determines thatthe signal pipe has a sufficient gain; conversely, ifGain_(sum)<Th_(gain), then the receiver 84 determines that the signalpipe has insufficient gain and should not be used for transmitting arespective data symbol.

If, at step 432, the receiver 84 determines that all of the signal pipescorresponding to the transmit antennas 92 identified at either step 428or 430 have sufficient gain, then, at a step 434, the receiver selectsall of the previously identified transmit antennas 92 for transmittingrespective data symbols.

In contrast, if, at step 432, the receiver 84 determines that not all ofthe signal pipes corresponding to the transmit antennas 92 identified ateither step 428 or 430 have sufficient gain, then, at a step 436, thereceiver selects for transmitting respective data symbols only theidentified transmit antennas 92 whose corresponding signal pipes havesufficient gain.

Then, at a step 438, the receiver 84 sets the sizes (e.g., number ofbits) of the data symbols to be transmitted by the transmit antennas 92selected at either step 434 or 436 according the gains of the signalpipes corresponding to the selected transmit antennas. For example, if asignal pipe as a higher gain than another signal pipe, then the receiver84 may set the number of bits in the data symbol to be transmitted overthe former signal pipe higher than the number of bits in the data symbolto be transmitted over the latter signal pipe. For example, the receiver84 can use a “waterfall” procedure to set the data-symbol sizes asdescribed in Introduction to MIMO Communications, which was previouslyincorporated by reference. After setting the data-symbol sizes, thereceiver 84 sends to the transmitter 82 the identities of the selectedtransmit antennas 92 and the sizes of their respective data symbols. Thereceiver 84 can send this information to the transmitter via theantennas 94 (acting as transmit antennas) and 92 (acting as receiveantennas), and the transmitter 82 can recover this information using anestimated channel matrix Ĥ that the transmitter 82, then acting as areceiver, previously estimated.

Next, at a step 440, the transmitter 82 transmits to the receiver 84 viathe selected transmit antennas 92 respective data symbols each havingthe respective size set by the receiver 84 at step 438. Regarding theunselected transmit antennas 92, the transmitter 82 can deactivate them(i.e., send no signals via the unselected antennas), or can redundantlytransmit via one or more of these unselected antennas a data symbol thatthe transmitter is also transmitting via a selected transmit antenna.For example, suppose transmit antenna 92 ₁ is unselected, and thetransmitter 82 transmits a data symbol DS₀ via the selected transmitantenna 92 ₀. The transmitter 82 also can elect to transmit DS₀ via thetransmit antenna 92 ₁. Such redundant transmission of the data symbolDS₀ can increase, at the receiver 84, the total SNR of the MIMO-OFDMsignals carrying DS₀, and can allow the transmitter 82 to increase thesize of DS₀.

Still referring to FIG. 39, alternate embodiments of the procedure 420are contemplated. For example, the procedure 420 may include steps notdescribed herein, the procedure may omit one or more of the describedsteps, or the transmitter 82 and receiver 84 can perform the steps422-440 in an order that is different from the described order.Furthermore, the transmitter 82 can perform one or more of the steps424-438 in response to channel-state or other information that thereceiver 84 provides to the transmitter. Moreover, although described astransmitting different training symbols from the antennas 92 during atraining period, the transmitter 82 may transmit same training symbolsfrom two or more of the antenna 92 during a training period eitherserially or simultaneously.

FIG. 40 is a diagram of a MIMO-OFDM system 460, which includes twoMIMO-OFDM transmitter-receivers 462 and 464, and of the portion 466 ofthe communication channel between the transmitter-receivers, accordingto an embodiment. The transmitter-receivers 462 and 464 respectivelyinclude transmit-receive circuitry 468 and 470 and antennas 92 and 94,and the minimum spacings d₉ and d₁₀ between the antennas 92 and theantennas 94, respectively, are less than one half the wavelength

$\left( \frac{\lambda_{c}}{2} \right)$

of the MIMO-OFDM carrier signal at frequency f_(c). For examplepurposes, it is assumed that the transmitter-receiver 462 istransmitting MIMO-OFDM signals with the antennas 92, and that thetransmitter-receiver 464 is receiving the transmitted signals with theantennas 94, it being understood that the below description would besimilar if the transmitter-receiver 464 where transmitting the signalsand the transmitter-receiver 462 were receiving the signals.Furthermore, it is assumed that the number T of transmitting antennas 92is equal to the number R of receiving antennas 94. Moreover, it isassumed that each of the antennas 92 and 94 can be any type of antennasuch as those described above in conjunction with FIGS. 22-37, and thatthe antennas 92 and the antennas 94 can be configured in any type ofarray pattern such as those described above in conjunction with FIGS.12-21. In addition, each antenna 92 can be the same as, or differentfrom, one or more other antennas 92, and each antenna 94 can be the sameas, or different from, one or more other antennas 94. Furthermore, theantennas 92 can form a same type or a different type of array comparedto the type of array that the antennas 94 form.

In an embodiment, the system 460 can be the same as the system 80 of oneor more of FIGS. 7 and 12-21 but for the transmitter-receiver circuitry468 and 470 respectively including antenna-configuring circuits 472 and474. The transmitter-receiver circuits 468 and 470 also includeantenna-selector circuits 476 and 478, which can be the same as theantenna-selector circuit 114 of FIG. 8.

The antenna-configuring circuit 472 is configured to configure one ormore characteristics (e.g., radiation pattern, gain, phase, directivity,polarization, orientation, position) of each of the antennas 92.Therefore, during a transmission mode, the antenna-configuring circuit472 can configure the transmission profile that each antenna 92 presentsto the receive antennas 94. By configuring the transmission profiles ofthe antennas 92, the antenna-configuration circuit 472 can configure theantennas to increase the diversity of the channel, and thus to increasethe capacity C of the channel above its saturation capacityC_(saturation). Likewise, during a receiving mode, theantenna-configuring circuit 472 can configure the reception profile thateach antenna 94 presents to transmit antennas. By configuring thereception profiles of the antennas 92, the antenna-configuration circuit472 can configure the antennas to increase the diversity of the channel,and thus to increase the capacity C of the channel above its saturationcapacity C_(saturation).

The antenna-configuring circuit 472 can configure the radiation pattern,gain, phase, and directivity, either together or separately, of anantenna 92 by changing one or more physical parameters of the antenna.For example, if the antenna 92 is a multi-element antenna like themetamaterial antenna 300 of FIGS. 31-33, then the antenna-configuringcircuit 472 can select which of the antenna elements to activate and toinactivate to set the antenna radiation pattern, gain, phase, anddirectivity together or separately.

The antenna-configuring circuit 472 also can configure the polarizationof an antenna 92 by changing one or more physical parameters of theantenna. For example, if the antenna 92 is a multi-element antenna likethe metamaterial antenna 300 of FIGS. 31-33, then theantenna-configuring circuit 472 can select which of the antenna elementsto activate and to inactivate to set the antenna polarization. Or, ifthe antenna 92 is a polarized antenna like the antenna 252 of FIG. 26,then the antenna-configuring circuit 472 can move the components of theantenna relative to one another to change the polarization pattern ofthe antenna; for example, the antenna-configuring circuit can slide thecomponent 254 of the antenna 252 left or right relative to the component256, or can rotate the component 254 relative to the component 256 tochange the angle between the components 254 and 256.

Furthermore, the antenna-configuring circuit 472 can configure theorientation and position of an antenna 92 together or separately bychanging one or more physical parameters of the antenna. For example, ifthe antenna 92 is a multi-element antenna like the metamaterial antenna300 of FIGS. 31-33, then the antenna-configuring circuit 472 can selectwhich of the antenna elements to activate and to inactivate to set theeffective antenna orientation or position (e.g., make it appear as ifthe antenna has rotated about one of its axes or shifted its position).Or, if the antenna 92 is dipole like the antenna 210 of FIG. 22 or is apatch antenna like the antenna 260 of FIGS. 27-29, then theantenna-configuring circuit 472 can move the antenna or can rotate theantenna about one or more of its axes.

And the antenna-configuring circuit 474 is configured to configure oneor more characteristics (e.g., radiation pattern, gain, phase,directivity, polarization, orientation, position) of each of theantennas 94 in a similar manner.

Still referring to FIG. 40, alternate embodiments of the MIMO-OFDMsystem 460 are contemplated. For example, any of the alternateembodiments described above in conjunction with FIGS. 7 and 12-21 forthe MIMO-OFDM system 80 can be applicable to the MIMO-OFDM system 460 ofFIG. 40. Furthermore, the system 460 can include more than the twoMIMO-OFDM transmitter-receivers 462 and 464, such as where one of thetransmitter-receivers is a wireless 802.11 compatible router and theother transmitter-receivers are clients (e.g., WiFi enabled smartphones).

FIG. 41 is a flow diagram of a procedure 500, which the MIMO-OFDMtransmitter-receiver 462, the MIMO-OFDM transmitter-receiver 464, orboth the transmitter-receivers 462 and 464 can of FIG. 40 can use todetermine how many respective data symbols the transmitter-receiver 462can transmit simultaneously to the transmitter-receiver 464 during asingle symbol period, according to an embodiment. Although thetransmitter-receiver 462 is described as transmitting symbols to thetransmitter-receiver 464, it is understood that a description of thetransmitter-receiver 464 transmitting symbols to thetransmitter-receiver 462 would be similar. Furthermore, for examplepurposes, the transmitter-receiver 462 is referred to as thetransmitter, and the transmitter-receiver 464 is referred to as thereceiver. Moreover, although an action may be attributed to thetransmitter 462 or the receiver 464, it is understood that such actionis performed by circuitry on board the transmitter or receiver, such asthe transmitter-receiver circuitry 468 and the transmitter-receivercircuitry 470 of FIG. 40, other circuitry that is part of thetransmitter-receiver circuitry 468 or 470, or other circuitry that ispart of the transmitter 462 or the receiver 464.

In summary, if, by following the procedure 500, the receiver 464determines that the channel capacity C with a current antennaconfiguration is greater than or equal to a threshold level that isgreater than the saturation channel capacity C_(saturation), then itnotifies the transmitter 462 to transmit data symbols using the currentantenna configuration; otherwise, the receiver causes one or more of theantennas 92 and 94 to be reconfigured in an attempt to increase thechannel capacity, at least up to a set number of iterations.

In more detail, first, at a step 502, the transmitter 462 transmitsrespective training symbols from each of the antennas 92, where each ofthe training symbols is different rom the other training symbols. Thetransmitter 462 may transmit each of the training symbols serially,i.e., at separate times, or may transmit the training symbolssimultaneously such as described above in conjunction with FIGS. 3-4.Sending different training symbols helps the receiver 464 betterdetermine from which transmit antenna 92 the transmitter 462 transmittedeach training symbol, particularly when the transmitter transmits thetraining symbols simultaneously. Alternatively, the transmitter 462 cantransmit same training symbols from two or more of the antennas 92.

Next, at a step 504, the receiver 464 estimates the channel matrix Ĥ.

Then, at a step 506, the receiver 464 determines whether the estimatedchannel matrix Ĥ is effectively full rank as described above inconjunction with FIG. 6. That is, the receiver 464 determines which ofthe transmit antennas 92 it can distinguish by determining whichrows/columns of the estimated channel matrix Ĥ are effectively linearlyindependent from one another. If all rows/columns of the estimatedchannel matrix Ĥ are effectively linearly independent from one another,then the estimated channel matrix is effectively full rank.

If, at the step 506, the receiver 464 determines that the estimatedchannel matrix is not effectively full rank, then the receiver proceedsalong a path of the procedure 500 that culminates in a reconfigurationof one or more of the antennas 92 and 94 in an effort to cause theestimated channel matrix to be effectively full rank. More specifically,the receiver 464 proceeds to a step 508, at which the receiveridentifies the one or more transmit antennas 92 that the receiver candistinguish; that is, the receiver identifies the one or more transmitantennas that are associated with rows/columns of the estimated channelmatrix Ĥ that are effectively linearly independent from the otherrows/columns of Ĥ. Next, at a step 510, the receiver 464 determines thegains of the signal pipes that correspond to the transmit antennas 92identified at the step 508, and determines whether each gain is largeenough to provide a sufficient SNR at the receiver. For example, thereceiver 464 can determine the gain of a signal pipe by calculating asum Gain_(sum) of the gains over all of the subchannels that form thesignal pipe (i.e., all of the subchannels associated with the transmitantenna 92 corresponding to the signal pipe), and then by comparing thissum to a threshold Th_(gain). If Gain_(sum)≧Th_(gain), then the receiver464 determines that the signal pipe has a sufficient gain; conversely,if Gain_(sum)<Th_(gain), then the receiver 464 determines that thesignal pipe has insufficient gain and should not be used to transmit arespective data symbol (the receiver can select, or be programmed with,a value for Th_(gain) corresponding to the application or to otherconventional criteria). The receiver 464 then proceeds to a step 520,which is described below.

In contrast, if, at the step 506, the receiver 464 determines that theestimated channel matrix is effectively full rank, then the receivercontinues along a procedural path in which the current antennaconfiguration is deemed to provide a sufficient channel capacity. Morespecifically, the receiver 464 proceeds to a step 514, at which thereceiver identifies all of the transmit antennas 92 as beingdistinguishable at the receiver, and, then proceeds to a step 516, atwhich the receiver determines the gains of the signal pipes thatrespectively correspond to all of the transmit antennas 92; the receivercan determine the gains of the signal pipes in a manner similar to thatdescribed above in conjunction with the step 510.

Next, at a step 518, the receiver 464 determines whether the gain ofeach signal pipe is sufficient to provide, at the receiver, a SNR thatis large enough for the receiver to recover a data symbol from theMIMO-OFDM signal transmitted over the signal pipe. For example, thereceiver 464 can determine whether a signal pipe has sufficient gain ina manner similar to that described above in conjunction with the step510.

If, at the step 518, the receiver 464 determines that not all of thesignal pipes have sufficient gain, then the receiver proceeds along theprocedural path that culminates in a reconfiguration of one or more ofthe antennas 92 and 94 in an effort to cause each of the signal pipes tohave a sufficient gain. More specifically, the receiver 464 proceeds toa step 520, at which the receiver selects only the transmit antennas 92that were identified in the step 508 or in the step 514 and thatcorrespond to signal pipes having sufficient gain. Then, at a step 522,the receiver 464 determines a difference Gain_(diff) between the highestand lowest gains of the signal pipes corresponding to the antennas 92selected at the step 520; as discussed below in conjunction with steps526 and 528, Gain_(diff) is an indication of the channel capacity C.Next, the receiver 464 proceeds to a step 524, which is described below.

In contrast, if, at the step 518, the receiver 464 determines that allof the signal pipes corresponding to all of the transmit antennas 92have sufficient gain, then, at a step 526, the receiver determines thedifference Gain_(diff) between the highest and lowest gains of thesignal pipes corresponding to the all of the antennas 92, and, at a step528, compares Gain_(diff) to a threshold Th_(Gaindiff). As describedabove in conjunction with FIG. 6, the capacity of the communicationchannel is typically highest when the signal pipes with sufficient gainhave similar gains (i.e., when the eigen values of the singular valuedecomposition of the channel matrix are equal to one another), ascompared to one or more signal pipes having relatively large gains andother signal pipes having significantly lower gains. For example, ifTh_(gain)=1 and there are four signal pipes with sufficient gain, thenthe four signal pipes having normalized gains of 5, 5, 5, 5(Gain_(diff)=0) typically provide a higher channel capacity than do thefour signal pipes having normalized gains 100, 2, 1.5, 1.3(Gain_(diff)=98.7). Consequently, as discussed below, ifGain_(diff)>_(Gaindiff); then the receiver 464 can cause one or both ofthe antenna configuring circuits 472 and 474 to reconfigure thecharacteristics of one or more of the antennas 92 and 94 in an effort toimprove the channel capacity by reducing the difference Gain_(diff)between the gains of the signal pipes with the highest and lowest gains.

If, at the step 528, the receiver 464 determines thatGain_(diff)>Th_(Gaindiff), then the receiver proceeds along theprocedural path that culminates in a reconfiguration of one or more ofthe antennas 92 and 94 in an effort to cause Gain_(diff)≦Th_(Gaindiff)More specifically, the receiver 464 proceeds to the step 524, at whichthe receiver saves the current antenna configuration, the selected onesof the transmit antennas 92 for the current antenna configuration, andGain_(diff) for the current antenna configuration in a memory circuitthat can be part of the transmitter-receiver circuitry 470. Next, at astep 530, the receiver 464 determines whether the number AntConfig ofantenna configurations analyzed in the above manner exceeds a thresholdnumber Th_(Configuration) _(_) _(number). IfAntConfig>Th_(configuration) _(_) _(number), then the receiver 464proceeds to a step 532, which is described below. In contrast, if IfAntConfig≦Th_(Configuration) _(_) _(number), then the receiver 464proceeds to a step 534.

At the step 534, the receiver 464 causes one or more of the antennas 92and 94 to be reconfigured in an effort to increase the channel capacityC by improving one or more of the effective rank of the estimatedchannel rank, the number of signal pipes with sufficient gain, and thedifference Gain_(diff) between the gains of the available signal pipeswith the highest and lowest gains (“available” means that the signalpipes correspond to a transmit antenna 92 that is distinguishable at thereceiver 464 and that has sufficient gain). More specifically, thereceiver 464 can cause the antenna configuring circuit 474 to alter oneor more reception characteristics (e.g., radiation pattern, gain,directivity, phase, polarization, orientation, location) of one or moreof the antennas 94, and can send a signal (e.g., using a previouslyestimated channel matrix between the receiver 464 acting as atransmitter and the transmitter 462 acting as a receiver) to thetransmitter 462 to cause the antenna configuring circuit 472 to alterone or more transmission characteristics of one or more of the antennas92. The antenna configuring circuits 472 and 474 can respectively alterthe characteristic of an antenna 92 and 94, respectively, according toany suitable algorithm. For example, the circuits 472 and 474 may alterthe characteristic of an antenna 92 and 94, respectively, in a randommanner, or according to a stored algorithm that takes into account,e.g., the channel state information (i.e., values of elements of theestimated channel matrix Ĥ), the application in which the transmitter462 and receiver 464 are being used, or a statistical analysis of thechannel state information over time.

Next, at a step, 536, the receiver 464 increments AntConfig.

Then, the receiver 464 returns to the step 502 to repeat theabove-described portion of the procedure 500.

Referring again to step 530, If AntConfig>Th_(Configuration) _(_)_(number), then at a step 532, the receiver 464 causes the antennaconfiguring circuits 472 and 474 to configure the antennas 92 and 94 inthe best antenna configuration that the receiver previously analyzed andsaved. The receiver 464 can determine which of the saved antennaconfigurations is best according to any suitable algorithm. For example,the best antenna configuration can be the configuration that yields thehighest channel capacity C, or the highest number of available signalpipes (in the case of multiple configurations yielding a same highestnumber of available signal pipes, the best configuration can be the onewith the lowest value of Gain_(diff)).

Next, at a step 538, the receiver 464 sends to the transmitter 462 asignal that causes the antenna-selector circuit 476 to select thetransmit antennas 92 that were selected in the best saved antennaconfiguration. Then the receiver 464 proceeds to a step 540.

Referring again to step 528, if Gain_(diff)≦_(Gaindiff), then thereceiver 464 also proceeds to the step 540.

That is, the receiver 464 proceeds to step 540 under the following twoconditions: 1) the number of tried antenna configurations exceeds athreshold number (AntConfig>Th_(Configuration) _(_) _(number)), or 2)the receiver 464 finds a configuration that provides an estimatedchannel matrix that is effective full rank, sufficient gain for allsignal pipes, and Gain_(diff)≦Th_(Gaindiff).

At the step 540, the receiver 464 sets the sizes (e.g., number of bits)of the respective data symbols to be transmitted by the selectedtransmit antennas 92 according the gains of the signal pipescorresponding to the selected transmit antennas. For example, if asignal pipe has a higher gain than another signal pipe, then thereceiver 464 can set the number of bits in the data symbol to betransmitted over the former signal pipe higher than the number of bitsin the data symbol to be transmitted over the latter signal pipe. Forexample, the receiver 464 can use a “waterfall” procedure to set thedata-symbol sizes as described in Introduction to MIMO Commnunications,which was previously incorporated by reference. After setting the symbolsizes, the receiver 464 sends to the transmitter 462 the identities ofthe selected transmit antennas 92 and the sizes of their respective datasymbols. The receiver 464 may send this information to the transmitter462 via the antennas 94 (acting as transmit antennas) and 92 (acting asreceive antennas), and the transmitter 462 may recover this informationusing an estimated channel matrix that the transmitter 462, then actingas a receiver, previously estimated.

Next, at a step 542, the transmitter 462 transmits to the receiver 464via the selected transmit antennas 92 respective data symbols eachhaving the respective size set by the receiver 462 at step 540.Regarding the unselected transmit antennas 92 (if any are unselected),the transmitter 462 can deactivate them (i.e., send no signals via theunselected antennas), or can transmit redundantly via one or more ofthese unselected antennas a data symbol that the transmitter is alsotransmitting via a selected transmit antenna. For example, suppose thetransmit antenna 92 ₁ is unselected, and the transmitter 462 transmits adata symbol DS₀ via the selected transmit antenna 92 ₀. The transmitter462 also can elect to transmit DS₀ via the transmit antenna 92 ₁. Suchredundant transmission of DS₀ can increase, at the receiver 464, the SNRof the MIMO-OFDM signals carrying DS₀, and can allow the transmitter 462to increase the size of DS₀.

Still referring to FIG. 41, alternate embodiments of the procedure 500are contemplated. For example, the procedure 500 may include steps notdescribed herein, the procedure may omit described steps, and thetransmitter 462 and receiver 464 may perform the steps 502-540 in anorder that is different from the described order. Furthermore, thetransmitter 462 can perform one or more of the steps 504-540 in responseto channel-state and other information that the receiver 464 provides tothe transmitter. Moreover, the receiver 464 can perform the procedure500 before each data symbol to be transmitted by the transmitter 462, orcan perform the procedure periodically such as described above inconjunction with FIG. 4. In the latter case, instead of iterativelyperforming the procedure 500 to determine the best antenna configurationfor the current channel conditions, the receiver 464 can save a suitableprior number (e.g., 10, 100, 300) of estimated channel matrices, formand continually update a statistical representation (e.g., an average)of the channel over time using these estimated channel matrices,determine a suitable antenna configuration for this statisticalrepresentation, and then cause the antenna-configuration circuits 472and 474 to configure the antennas 92 and 94, respectively, in thedetermined configuration.

From the foregoing it will be appreciated that, although specificembodiments have been described herein for purposes of illustration,various modifications may be made without deviating from the spirit andscope of the disclosure. Furthermore, where an alternative is disclosedfor a particular embodiment, this alternative may also apply to otherembodiments even if not specifically stated.

For example, any circuitry described above (e.g., thetransmitter-receiver circuitry 68, 70, 468, and 470 of FIGS. 7, 12-21,and 40, respectively) can be formed from integrated-circuit components(e.g., transistors, resistors, capacitors, inductors, diodes) that arededicated to performing the functions of the circuitry, can be formedfrom circuitry, such as microprocessor circuitry, that is configured toexecute instructions to perform the circuit functions, can be formedfrom circuitry, such as field-programmable-gate-array circuitry, that isconfigurable with firmware to perform the circuit functions, or can beformed from a combination or subcombination of dedicated,instruction-executing, and firmware-configurable circuitry. In the casewhere at least some of the circuitry is instruction-executing orfirmware-configurable, the corresponding instructions and firmware canbe stored on a tangible, non-transitory computer-readable medium such asFLASH, RAM, or other types of electronic memory, a magnetic or anoptical storage medium, or any other suitable type of a storage medium.

Furthermore, the MIMO-OFDM systems 80 and 460 of FIGS. 7, 12-21, and 40may include any number of, and any suitable type of,transmitter-receivers 82, 84, 462, and 484, such as computers, laptops,tablets, smart phones, vehicles, medical devices and monitors, and itemsbelonging to the Internet of Things (IoT).

Moreover, although the MIMO-OFDM systems 80 and 460 of FIGS. 7, 12-21,and 40 are described as including antennas 92 and 94 that are spacedapart from adjacent antennas by a minimum distance of less than

$\frac{\lambda_{c}}{2},$

these systems may still provide an increased channel capacity when thisminimum distance is greater than or equal to

$\frac{\lambda_{c}}{2}.$

This is because even with this spacing, and regardless of whether thereceiver is in the far field of the transmitter, the diversity of thechannel portion between the transmit and receive antennas may be, byitself, insufficient to provide an estimated channel matrix of effectivefull rank, and to provide all signal pipes having sufficient gain.

While various aspects and embodiments have been disclosed herein, otheraspects and embodiments will be apparent to those skilled in the artfrom the detailed description provided herein. The various aspects andembodiments disclosed herein are for purposes of illustration and arenot intended to be limiting, with the true scope and spirit beingindicated by the following claims.

This disclosure has been made with reference to various exampleembodiments. However, those skilled in the art will recognize thatchanges and modifications may be made to the embodiments withoutdeparting from the scope of the present disclosure. For example, variousoperational steps, as well as components for carrying out operationalsteps, may be implemented in alternate ways depending upon theparticular application or in consideration of any number of costfunctions associated with the operation of the system; e.g., one or moreof the steps may be deleted, modified, or combined with other steps.

Additionally, as will be appreciated by one of ordinary skill in theart, principles of the present disclosure, including components, may bereflected in a computer program product on a computer-readable storagemedium having computer-readable program code means embodied in thestorage medium. Any tangible, non-transitory computer-readable storagemedium may be utilized, including magnetic storage devices (hard disks,floppy disks, and the like), optical storage devices (CD-ROMs, DVDs,Blu-ray discs, and the like), flash memory, and/or the like. Thesecomputer program instructions may be loaded onto a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructionsthat execute on the computer or other programmable data processingapparatus create a means for implementing the functions specified. Thesecomputer program instructions may also be stored in a computer-readablememory that can direct a computer or other programmable data processingapparatus to function in a particular manner, such that the instructionsstored in the computer-readable memory produce an article ofmanufacture, including implementing means that implement the functionspecified. The computer program instructions may also be loaded onto acomputer or other programmable data processing apparatus to cause aseries of operational steps to be performed on the computer or otherprogrammable apparatus to produce a computer-implemented process, suchthat the instructions that execute on the computer or other programmableapparatus provide steps for implementing the functions specified.

The foregoing specification has been described with reference to variousembodiments. However, one of ordinary skill in the art will appreciatethat various modifications and changes can be made without departingfrom the scope of the present disclosure. Accordingly, this disclosureis to be regarded in an illustrative rather than a restrictive sense,and all such modifications are intended to be included within the scopethereof. Likewise, benefits, other advantages, and solutions to problemshave been described above with regard to various embodiments. However,benefits, advantages, solutions to problems, and any element(s) that maycause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, a required, or anessential feature or element. As used herein, the terms “comprises,”“comprising,” and any other variation thereof are intended to cover anon-exclusive inclusion, such that a process, a method, an article, oran apparatus that comprises a list of elements does not include onlythose elements but may include other elements not expressly listed orinherent to such process, method, system, article, or apparatus.

In an embodiment, the system is integrated in such a manner that thesystem operates as a unique system configured specifically for functionof the device, and any associated computing devices of the systemoperate as specific use computers for purposes of the claimed system,and not general use computers. In an embodiment, at least one associatedcomputing device of the system operates as specific use computers forpurposes of the claimed system, and not general use computers. In anembodiment, at least one of the associated computing devices of thesystem are hardwired with a specific ROM to instruct the at least onecomputing device.

The following references are incorporated by reference:

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1. A transmitter, comprising: a first number of antennas each spacedfrom another of the antennas by approximately a distance and configuredto provide, at one or more wavelengths that are greater than twice thedistance, a channel capacity that exceeds a channel capacity that thefirst number of antennas would provide if each of the first number ofantennas were to have a same transmission profile; and a signalgenerator configured to generate a second number of signals each havinga wavelength that is greater than twice the distance, the second numberrelated to a third number of signal pipes; and to couple each of thesecond number of signals to a respective one of the antennas.
 2. Thetransmitter of claim 1 wherein the first number of antennas form atleast part of an antenna array.
 3. The transmitter of claim 1 wherein atleast two of the first number of antennas comprise a metamaterial. 4.The transmitter of claim 1 wherein: one of the first number of antennasis configured to have a first transmission characteristic; and anotherone of the first number of antennas is configured to have a secondtransmission characteristic that is different from the firsttransmission characteristic.
 5. The transmitter of claim 4 wherein: thefirst transmission characteristic includes a first radiation pattern;and the second transmission characteristic includes a second radiationpattern that is different from the first radiation pattern. 6-16.(canceled)
 17. The transmitter of claim 4 wherein: the firsttransmission characteristic includes a first directivity; and the secondtransmission characteristic includes a second directivity that isdifferent from the first directivity. 18-20. (canceled)
 21. Thetransmitter of claim 4 wherein: the first transmission characteristicincludes a first orientation; and the second transmission characteristicincludes a second orientation that is different from the firstorientation. 22-23. (canceled)
 24. The transmitter of claim 4 whereineach antenna has at least one transmission characteristic that isselected to maximize the effective rank of the channel matrix.
 25. Thetransmitter of claim 4 wherein each antenna has at least one orientationangle that is selected to maximize the effective rank of the channelmatrix. 26-28. (canceled)
 29. The transmitter of claim 1 wherein thefirst number of antennas are arranged substantially in a one-dimensionalarray. 30-35. (canceled)
 36. The transmitter of claim 1 wherein thefirst number of antennas are arranged substantially in a two-dimensionalarray.
 37. The transmitter of claim 1 wherein the first number ofantennas are arranged substantially in a three-dimensional array. 38.The transmitter of claim 1 wherein the first number of antennas arearranged in at least first and second groups, none of the antennas inthe first group closer than half of the wavelength to any of theantennas in the second group. 39-43. (canceled)
 44. The transmitter ofclaim 1 wherein each of the first number of antennas has a respectivedimension that is significantly smaller than one half of the wavelength.45-64. (canceled) 65.-102. (canceled)
 103. A method, comprising:generating a first number of signals each having a wavelength that isgreater than twice a distance, the first number related to a secondnumber of signal pipes of a channel having a capacity; and transmittingeach of the first number of signals over the channel with a respectiveone of a third number of antennas each spaced from another of theantennas by approximately the distance such that the capacity of thechannel exceeds a channel capacity that the third number of antennaswould provide if each of the third number of antennas were to have asame transmission profile. 104-105. (canceled)
 106. The method of claim103 wherein transmitting each of the first number of signals includes:transmitting one of the first number of signals according to a firsttransmission characteristic; and transmitting another one of the firstnumber of signals according to a second transmission characteristic thatis different from the first transmission characteristic. 107-125.(canceled)
 126. The method of claim 106, further comprising selectingfor each antenna at least one transmission characteristic to maximizethe effective rank of the channel matrix.
 127. The method of claim 106,further comprising selecting for each antenna at least one orientationangle to maximize the effective rank of the channel matrix. 128-183.(canceled)
 184. The method of claim 103, further including: receivingchannel information from a source remote from the third number ofantennas; and determining the second number in response to the channelinformation. 185-191. (canceled)
 192. The method of claim 103, furthercomprising configuring at least one of the third number of antennas inresponse to the second number of signal pipes having a relationship to atarget number of signal pipes. 193-202. (canceled)
 203. A tangiblecomputer-readable medium storing instructions that, when executed by acomputing machine, cause the computing machine, or circuitry undercontrol of the computing machine: to generate a first number of signalseach having a wavelength that is greater than twice a distance, thefirst number related to a second number of signal pipes of a channelhaving a capacity; and to transmit each of the first number of signalsover the channel with a respective one of a third number of antennaseach spaced from another of the antennas by approximately the distancesuch that the capacity of the channel exceeds a channel capacity thatthe third number of antennas would provide if each of the third numberof antennas were to have a same transmission profile. 204-303.(canceled)
 304. A transmitter, comprising: a first number of antennaseach spaced from another of the antennas by approximately a distance andconfigured to provide, at one or more wavelengths that are greater thantwice the distance, a channel capacity that exceeds a channel capacitythat the first number of antennas would provide if each of the firstnumber of antennas were to have a respective directivity that is nohigher than a directivity of a dipole antenna; and a signal generatorconfigured to generate a second number of signals each having awavelength that is greater than twice the distance, the second numberrelated to a third number of signal pipes; and to couple each of thesecond number of signals to a respective one of the antennas.
 305. Amethod, comprising: generating a first number of signals each having awavelength that is greater than twice a distance, the first numberrelated to a second number of signal pipes of a channel having acapacity; and transmitting each of the first number of signals over thechannel with a respective one of a third number of antennas each spacedfrom another of the antennas by approximately the distance such that thecapacity of the channel exceeds a channel capacity that the third numberof antennas would provide if each of the third number of antennas wereto have a respective directivity that is no higher than a directivity ofa dipole antenna.
 306. A tangible computer-readable medium storinginstructions that, when executed by a computing machine, cause thecomputing machine, or circuitry under control of the computing machine:to generate a first number of signals each having a wavelength that isgreater than twice a distance, the first number related to a secondnumber of signal pipes of a channel having a capacity; and to transmiteach of the first number of signals over the channel with a respectiveone of a third number of antennas each spaced from another of theantennas by approximately the distance such that the capacity of thechannel exceeds a channel capacity that the third number of antennaswould provide if each of the third number of antennas were to have arespective directivity that is no higher than a directivity of a dipoleantenna.